Optimizing Skateboard Lean Steer Physics

Final Report Submitted in partial fulfillment of the requirements for ENGS 90: Engineering Design Methodology and Project Completion

Optimizing Skateboard Lean Steer Physics March 14, 2023

Sponsored by

Lean Steer Difference, LLC. Project Team 6 Cameron Wolfe Connor Coale Diego Barrutia Onyedika Onuorah Phyo Pyi Kyaw Youssef Marzouk

Faculty Advisors Minh Phan, Chris Magoon

Abstract To address the inherent instability of skateboards, our team collaborated with Lean Steer Difference LLC. to develop their concept of a dynamically actuated skateboard. The board considers both speed and the rider’s tilt angle to determine the optimal turning radius, balancing centripetal acceleration with the force of gravity on the rider. To achieve this, the board incorporates three major design innovations that depart from a standard skateboard. First, it breaks away from the typical design of skateboard kingpin trucks—the parts that connect the wheels to the board—to create a new design that decouples leaning and steering. Second, it utilizes a combination of sensors and software to determine the speed and tilt angle of the board, which it uses to calculate the optimal turning radius. Finally, the board uses this turning radius to steer the trucks with motors to the necessary turning angles. Our team integrated these innovations into an initial prototype, and we also developed a testing rig that can be attached to any skateboard. This testing rig allows us to simulate a rider on the board safely while collecting data on the dynamics and operation of the board. With this setup, we could quantify the behavior of standard trucks and compare it to our new trucks. Additionally, our sponsor can continue testing using the test rig after we conclude our portion of the project. Finally, all our work includes the necessary documentation for the continued development of the technology by a new team.

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Contents Executive Summary

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1 Introduction 1.1 Problem Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.2 Value Proposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.3 Societal Context . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6 6 6 6

2 Ideation 2.1 Baseplate Angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.2 Electrical vs Mechanical . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.3 Full Actuation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.3.1 Gears . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.3.2 Cam Actuation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7 8 8 8 8 8

3 Deliverables 3.1 Test Rig . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.1.1 Mechanical Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.1.2 Electrical Design and Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.1.3 Software Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.2 Truck Mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.2.1 Return to Center (RTC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.2.2 Actuation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.2.3 Combination of Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.3 Truck Electronics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.3.1 Motors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.3.2 Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.4 Truck Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.5 Filtering and Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.5.1 Extended Kalman Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.5.2 Optimal Lean Steer Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.5.3 Feedback Motor Controller . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.6 Bench Top Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

9 9 9 10 10 11 11 12 12 13 13 13 16 17 17 21 22 23

4 Economic Analysis

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5 Recommendations for Future Work 5.1 Test Rig . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5.2 Mechanical . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5.2.1 Return to Center Mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . .

5.2.2 Hanger Actuation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5.3 Electrical . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5.3.1 One Battery with Voltage Conversion . . . . . . . . . . . . . . . . . . . . . .

5.4 Controls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5.4.1 Extended Kalman Filter Improvements . . . . . . . . . . . . . . . . . . . . .

5.4.2 Motor Controller Improvements . . . . . . . . . . . . . . . . . . . . . . . . . .

5.5 Potential Future 89/ 90 Projects . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5.5.1 Trucks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

26 26 27 27 28 28 28 29 29 30 30 30

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5.5.2

Electronics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

A References

31

B Figures in Report

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C Additional Figures C.1 Baseplate Angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

C.2 Tulip Prototype for Torque Verification . . . . . . . . . . . . . . . . . . . . . . . . .

C.3 FEA of Truck Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

C.4 Aluminum Truck . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

C.5 Block Diagram for Code of Both Systems . . . . . . . . . . . . . . . . . . . . . . . .

33 33 34 35 36 37

D Tables in Report

38

E Moment of Ineria

39

F Parameters for Extended Kalman Filter

39

G Net Present Value Analysis

40

H Testing Rig Documentation

41

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Executive Summary Significance Skateboards and electric skateboards have gained popularity in the past years for both recreation and commuting. Modern boards have a simple design comprising of a board mounted to mechanical trucks which hold the wheels. Other lean-to-steer devices, which include snowboards, skis, surfboards, and bikes, rely on a combination of tilt angle, speed, and ground edge contact when steering. Skateboards do not have edges. Instead, they have two pairs of wheels that remain on the ground at all times and are turned based on the board’s tilt. This discrepancy, along with turning the same amount regardless of speed, leads to noticeably different steering performance.

Skateboarders may find a truck that emulates the user experience of other lean-to-steer devices to be preferable to the existing truck technology.

Objectives With an understanding of the differences between lean-to-steer devices and skateboards, we aim to develop a new truck design that aligns more closely with optimized lean-steer physics, as demonstrated in the previously mentioned lean-to-steer devices. Additionally, we plan to evaluate the performance of existing trucks to compare the user experience of these trucks with the trucks we designed.

Innovation As recreational riders and commuters aim to ride faster on their skateboards, there is an opportunity to provide them with a safer and more enjoyable riding experience. Developing trucks that more closely follow the lean-steer physics of other lean-to-steer devices can help us achieve these goals.

Approach To achieve this, our team has developed a combined electrical-mechanical system that measures the rider’s speed and tilt angle to determine how much the board should turn. This is accomplished using various sensors, such as Inertial Measurement Units, Tachometers, and encoders, that collect board data. These data are then processed by algorithms, including a dynamical model of a skateboarder, to determine the optimal turning radius at any given state. The turning radius is then used to actuate custom-designed skateboard trucks that decouple leaning and steering.

Impact The proposed solution has the potential to revolutionize the skateboard industry, making it a viable transportation option for the first and last mile of public transportation commuters. It would reduce traffic congestion, improve air quality, and save individuals money on buying and maintaining personal vehicles. Furthermore, the proposed solution has the potential to encourage the adoption of electric skateboards by pedestrians and increase the accessibility of road infrastructure through micro-mobility, resulting in significant environmental benefits.

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1

Introduction

1.1

Problem Definition

Like other lean-steer platforms (such as bikes, skis, and surfboards), skateboards are inherently unstable. Much like an inverted pendulum, gravity will cause them to fall over unless they are perfectly upright. To counteract this, a restorative force is needed to balance the force of gravity and return the rider to an upright position. This force comes from turning, which causes the rider to experience centripetal acceleration, pulling them upright. These two counteracting forces allow the rider to reach a stable equilibrium at a certain lean angle. This principle is known as ”optimal lean-steer physics” and is the governing principle behind most lean-steer vehicles, with one notable exception: the skateboard.

The turning radius of a skateboard is determined entirely by the board’s tilt. However, the centripetal acceleration experienced while turning is affected by both velocity and turning radius.

This means that skateboard riders cannot take advantage of optimal lean-steer physics, as the same amount of tilt produces vastly different centripetal accelerations at different speeds. Additionally, the board becomes much more reactive at high speeds; a slight tilt in the board’s angle causes significant acceleration, which can throw the rider off the board or lead to issues like speed wobble.

1.2

Value Proposition

Our solution proposes a turning mechanism for skateboards that enables riders to use the full leaning range of the board at all speeds by dynamically adjusting the turning radius in response to changes in speed and tilt angle. By doing so, we can improve the control dynamics of skateboards at higher speeds, which can otherwise pose safety concerns and technical limitations for riders.

The key objectives of the proposed solution include designing a test rig to characterize skateboard stability with respect to different board and rider parameters and implementing sensing, control, and actuation systems that enable riders to use the full leaning range of the board at all speeds.

The potential real-world applications of this solution include transportation, pure recreation, and professional skateboarding. The advantages of our proposed solution in the market are that it provides a combination of (1) a full leaning range of the board and (2) an actuated turning mechanism that dynamically adjusts the turning radius based on tilt angle and velocity to more closely align with lean steer physics. Currently, there are products in the market that address (1), such as Waterborne Skateboards, and (2), such as damping systems for skateboards (Jeremy Fox US8752849B1)[1], but do not address both.

In cities with public transportation infrastructure, the proposed solution aims to tackle the first mile/last mile (FM/LM) problem. The first mile refers to the initial part of an individual’s trip from the starting point, often their home or workplace, to the public transport station, while the last mile is the final part of the individual’s trip from the transportation station to their ultimate destination. An optimized lean steer skateboard, which our project aims to create, will enable riders to complete the first and last parts of their journey at a faster pace and lower cost, thereby increasing the adoption of public transportation.

1.3

Societal Context

From a societal perspective, the proposed solution has the potential to encourage the adoption of electric skateboards by pedestrians and increase the accessibility of road infrastructure through micro-mobility. With no noise and low emissions, there would be substantial environmental benefits. This would lead to improved air quality in cities by reducing commuter-associated pollution.

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Figure 1: First Mile Last Mile Problem Furthermore, the proposed solution would address the FM/LM dilemma and change how people approach public transportation, resulting in more efficient and equitable public transportation.

According to recent Census Bureau findings, just over 46% of all public transportation commuters prefer to take buses instead of other forms of travel[2]. However, transit stops often only provide transportation to high-traffic locations, leaving many commuters to walk the first or last leg of their trip. The proposed solution provides a mode of transportation that can bridge this distance. This micro-mobility contributes to easing traffic by offering an alternative to using personal vehicles.

The cost of the proposed solution would also help individuals save money on the cost of buying a car, maintenance, and parking. People would have a quicker and more efficient option than walking a long way or getting stranded far from work or home.

The downside to the proposed solution is that the individuals would prefer riding skateboards on the road since the ride is more stable at higher speeds. However, traffic laws for skateboarding on the road aren’t as well defined as bicycle or in-line skating which encourages risky behavior such as not following stop signs or helmet rules. Therefore, it poses risks to the riders as well as the drivers who might not be aware of the speed capable of electric skateboards. Moreover, if the individuals chose to ride on pavements, it poses risks again to the riders as well as the pedestrians who might not have surrounding awareness. The proposed solution can also encourage the production of lithium which can be environmentally devastating when mined.

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Ideation

We explored many different avenues that would allow us to accomplish this dynamic change of lean-steer ratios. LSD wanted a solution that was compatible with current skateboards, which led us to focus on creating a truck system that would be mountable to any skateboard using the standard skateboard bolt-hole pattern.

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2.1

Baseplate Angle

Currently, skateboard riders can opt for reducing the responsiveness of the skateboard’s turning to their leaning by buying trucks of different baseplate angles. Baseplate angle refers to the angle of the hanger relative to the board. The baseplate angle will range from 0 to 90◦ . The lower the baseplate angle, the less responsive the trucks will be, while higher baseplate angles result in more responsive rides and require increased rider sensitivity. However, changing the baseplate angle does not address the main problem. Lower baseplate angles will reduce the rider’s experience of speed wobble, however, the lean-steer physics of the system remains not ideal. Furthermore, this change is not dynamic. The baseplate angle does not change with speed. We did explore dynamic baseplate angle adjustment as a solution but determined that we would need to push further to find an idea that solved the main problem at hand.

2.2

Electrical vs Mechanical

LSD’s current mechanical design (Fig. 4a) allows the rider to better optimize lean-steer physics at predetermined speeds by having interchangeable inserts (Fig. 4b). This design highlighted the problem we were observing: Purely mechanical solutions only solved lean-steer physics at chosen speeds without dynamically changing throughout the ride.

For electronic solutions, we explored ideas regarding baseplate angle adjustment with speed, a 3-bar linkage actuated by a motor, and a gear system actuated by a motor. We found that each idea brought its own complications from not solving the problem directly, to gear stripping under load. However, we were able to determine that we would need to separate leaning from steering to effectively tackle this problem. We give the rider access to the full leaning range of the board at all times, and through a control system we can determine the turning radius; dynamically adjusting the lean-steer ratio with speed through the control system. However, deformation under load was still an apparent problem.

2.3

Full Actuation

Actuating the hangers that control the turning radius of the board was a discussion we had many times as a team and with LSD. The solution’s complexity was increasing rapidly and we needed the simplest way to actuate the hangers to reduce any further increase in complexity. We decided to use a stepper motor for the positional accuracy it provides and the torque-to-size ratio that it offers. There would be a motor mounted on both trucks and they will work together to turn the board by providing their respective hanger angles.

2.3.1

Gears

When exploring hanger actuation, motor-actuated gears were the first avenue we explored.

Stripping of the gears became a major concern. A skateboard experiences heavy loads under use.

In current truck designs disturbances are usually handled by the rider and dampened by a bushing.

Gear actuation would eliminate all damping. In regular use the board does experience wear and deformation, however, this deformation is never detrimental to the functionality of the board. We needed a system that would tolerate moderate deformation and maintain functionality.

2.3.2

Cam Actuation

Along with LSD we decided that using the steering guide cam profile from their current mechanical design (Fig.4b) allows us to maintain turning functionality despite moderate deformation 8

from the followers, and provides resistance to disturbances such as vibrations and pebbles when riding. The cam profile provides a gear reduction which further improves the likelihood that the motor would be able to tolerate large disturbances during a ride.

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Deliverables

3.1

Test Rig

By decoupling leaning and steering, we remove the rider’s ability to directly steer the board mechanically. This carries significant risks, especially since the technology is still in its inception.

Any coding errors, sensor failures, or electrical failures would leave the user unable to steer the board mechanically. Furthermore, we would see the greatest improvements from the standard mechanical skateboard to our proposed actuated trucks at higher speeds. As a result, before we started to develop the trucks, we created a testing apparatus that allows us to test a skateboard at these higher speeds while mimicking a human’s weight and interaction with the board.

3.1.1

Mechanical Design

As stated previously, this testing apparatus needs to mimic a human rider. A normal skateboard will experience general oscillations if pushed in a straight line. Therefore, we need to provide our test rig’s ”human” rider–affectionately named Jerry–the means to correct for these oscillations independently. A human will do this by using their abdominals to stay upright, and their ankles to steer the board back on track. Furthermore, this test rig needed the capability of being driven and tested at moderately high speeds.

Our approach was as follows: To achieve the speeds necessary for effective testing, a car must be used. As such, there must be a component of the testing apparatus that can be secured to a car to guide it to these speeds. However, rigid mounting would result in skewed data as the arm would involuntarily prevent the board from oscillating naturally. We must create a car-mounted system that can only lightly guide the testing rig to stay upright. This provides a great point of contact for the ”abs”. We create two separate components, one that attaches to a car and another that attaches to a board. The board attachment will hold the body, or the main weight, that acts as the inverted pendulum and functions as the ”ankle”, while the car attachment will hold the body upright via surgical tubing to act as the abs.

The rider’s ankle will be simulated using 4 springs. The springs are relatively stiff but are only slightly less rigid than the truck bushings. This allows the springs to follow a similar stiffness to the bushings as more leaning is required and subsequently more force. This results in neither the bushings nor the springs fully engaging before the other engages. Two springs in the front and back will help simulate the weight distribution of a rider in acceleration and deceleration. For further guiding, the springs are held in cups and secured with screws to allow them to engage in extension and compression–reducing the required spring constant by half.

Pulleys are added to the truck attachment and board to allow for a safety bail. If the testing rig oscillates or will potentially fall, a rope will be all that is required to lift the board away from the street. A pulley reduction of 3 is shown in the model such that a single individual should be able to lift the board with relative ease. Height adjustability of the car attachment was also added to account for different suspension heights of cars that may be used. A custom surgical tubing attachment for the weight bar was created for ease of mounting and custom tensioning at a moment’s notice.

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Figure 2: SolidWorks of testing rig 3.1.2

Electrical Design and Sensors

The electrical portion of the testing rig must collect data from both its own sensors along with sensor data from the truck design being tested. For this reason, data must be passed between two Teensys – one on the test-rig and one on the truck – to track and validate the system’s performance.

This sort of data handshaking can be seen in appendix C.5. The two parts of the overall environment have their own sensors, but these and the algorithms that run on them must be tracked. This data is then written to an SD card onboard the testing rig’s Teensy.

The housing for the testing rig is seen below in figure 3.

(a) Housing CAD

(b) Housing on Testing Rig

Figure 3: Test Rig Housing For this specific housing, the top is an acrylic sheet that is laser-cut to fit a button that creates new files, debugging LED, and power toggle switch. The two 1/8in acrylic sheets on the side allow us to access the battery compartment, micro-SD, and micro-USB without penalizing water and dust resistance. This housing safely clamps to the test rig with the two legs at the bottom. The housing additionally has a one-way clamp to securely place the electronic circuit board. The system is made more water-resistant by using hot glue to seal the top and the tachometer slot.

3.1.3

Software Implementation

The software for the test rig is, on the whole, very simple. The aforementioned appendix C.5 shows a block diagram including the software flow for the test rig. The most important consideration is that the system writes a new batch of data to the SD card on a 60hz clock cycle. In order to achieve this, it must read through the serial receiving buffer specific to hardware Serial receiver 1.

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What this means is that the test rig is highly adaptable to any future design. An arbitrary future design must therefore have some means of communicating to the test rig via UART over Serial1, which has its RX and TX pins on Teensy pins 0 and 1. This is important to consider should sensor choice and implementation be altered. Generally speaking, data should be communicated in CSV format from a unit under test to the test rig. This is because CSV is a compact way to communicate the data, and it is easy to append test rig validation data (like the ultrasonic sensor’s reading, or others if implemented) for subsequent writing to the SD card.

This is described more in-depth in the actual code through comprehensive comments. A repository of all code will be delivered to LSD in a zip file along with this report. The code specific to the test rig is present in the test-rig subdirectory seen in figure 11.

3.2

Truck Mechanics

Lean Steer Difference came to us with a purely mechanical design for a truck that would allow customizable lean-steer ratio inserts. This lets the rider better optimize lean-steer physics at a predetermined speed. However, at speeds lower and higher than optimal, the rider would need to over or under-steer, respectively. This truck design was our starting point. The dynamic adjustability of lean-steer physics would be controlled by a motor, and control algorithm.

(a) Full mechanical unpinned truck

(b) Steering Guide

(c) Return to Center

Figure 4: Above are the main components of Lean Steer Difference’s original mechanical unpinned truck.

3.2.1

Return to Center (RTC)

Lean Steer Difference brought us a redesign concept of the return to center created by Helix Design in Manchester, NH. The design was based on Original Skateboards’ truck and follows the same concept but uses a high-constant spring rather than urethane. The concept by Helix Design uses a shallow cam profile that will compress a urethane cylinder as the board tilts. We would need to fabricate trucks in order to properly test the dynamic trucks, so we opted to create a prototype of the concept to verify the torque it was producing before redesigning and fabricating. The new design had much fewer parts and a lower profile, which we favored because the addition of a motor resulted in a lack of space under the board.

By mounting it on a test shaft and using a torque wrench we were able to validate the torque produced by the cam design to peaking at 29.5 oz-in of torque with no initial compression of a 11

95A urethane cylinder with an OD of 1 1/8” and ID of 0.5”(Appendix C.2). With the addition of the new RTC cam, this project now has 2 cam profiles; the first is associated with the turning of the hanger and is seen in Figure. 4b. To reduce confusion, we have used the following naming convention: RTC cam profile is now called the ”Tulip” and the truck hanger cam remains the ”cam”.

3.2.2

Actuation

As previously discussed, the turning of the hanger is guided by a cam (Fig. 4b). This cam profile was modified from optimizing lean-steer at a particular speed to be a smooth transition and allows for the whole steering range. For initial testing we gave the cam the ability to provide ±15◦ of rotation. This cam profile will have rollers that interact with it to rotate the hanger. The swept profile of the cam works such that the hanger has support from both sides. As one side of the cam pushes to turn, the other side gives an equal amount of space to maintain contact at all angles.

(a) Hanger cam

(b) Tulip Prototype

Figure 5: (a) Redesigned cam for ±15◦ of hanger rotation.(b) A prototype of the Tulip. This was an iteration that used a pin to keep the Tulip from rotating and was later replaced by a two-sided D shaft through hole.

We decided to mount the rollers on the truck hanger, and the cam to the motor because can properly secure the cam to the motor by way of set screw.

3.2.3

Combination of Mechanisms

Combining these two mechanisms while maintaining their independent movement was a complex task. The new RTC reduces parts but increases the complexity of the interactions between moving elements. The board needs to tilt around the RTC, but the RTC needs to slide to compress the urethane. Therefore, something needs to keep the RTC from rotating with the board. Helix Design had two small slots extending the length of the shaft to guide the Tulip, however, from testing with a steel prototype we felt that they would deform, and break, under a full load of a rider. We opted for a double-sided D shaft that extends the length of the truck. Despite the increased area provided by the double-D shaft, the RTC still produces a lot of torque, especially when preloaded

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for stiffer leaning. As a result, any plastic design would be short-lived before the deformation lead to breaking and excessive backlash. As such, we fabricated an aluminum truck to withstand leaning and testing under load. However, given time this aluminum truck will also deform. Tempering the aluminum may be a solution, but please see Section. 5.2 for recommendations about moving away from the current double-D design and to more robust solutions.

The shaft is a dead axle. It only supports the mechanisms rotating around it. As such it creates an optimal securing location for the mounting and housing of the motor and hanger. This housing is neutral. It does not spin or rotate with either hanger or board. With all of this in mind, we went through a few design iterations before landing on the design we fabricated and used for testing.

Rather than making a sleek design, we opted for a thicker and more robust look for testing. We performed Finite Element Analysis (FEA) on all of the load-bearing components, however, this system is still not fully characterized, and as such, we needed a design that was over-designed to provide the least likelihood of breaking. We performed a static analysis where a 200-pound person put all of their weight on one of the trucks, as well as simulating the oblique loads experienced during a turn. The results can be seen in Figures 24 and 25 of Appendix C.3.

(a)

(b)

Figure 6: (a) Prototype design of the electronic trucks and a section view of the components (b).

3.3 3.3.1

Truck Electronics Motors

The motor used in our system is a NEMA17 Stepper Motor available from McMaster. We wanted to have a high amount of holding torque while maintaining a small package size and accurate rotation capabilities. As seen on McMaster, this motor operates at 12-24V and has 125in-Oz. of torque. Although this motor was able to twist the hangers using the cam with no weight on the board, it struggled to do so with even a minor amount of weight being impressed upon the board.

Motor selection is certainly an aspect of the design that can be improved and will be explored in later sections of this document.

In order to power these motors, we opted to use the TMC2208 Stepper Driver. These are a low-cost, easy-to-use option for driving motors from 12-24V, which is what we were aiming to do with our aforementioned NEMA17 steppers. The two controllers used by the system can be seen in figure 7 with the blue heatsinks at the right.

3.3.2

Sensors

There are a few different sensors used to gather the necessary data used as inputs to the control loop. The data to be gathered includes ground speed, board orientation with respect to the horizon,

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Figure 7: Teensy with Gyro and Motor Controllers and the angle of the hangers relative to the board. All sensor datasheets are provided within the software handoff zip file under the docs subdirectory.

In order to measure board groundspeed, we used an OMRON EE-SX-672-WR Photomicrosensor. We acquired our sensor from Adafruit at this listing. The sensor transistor output nominally uses 5V, but by enabling a pull-up resistor internally on the Teensy, it is able to be used at 3.3V. The sensor is used on a digital input pin as a digital interrupt, and each time an interrupt is received a counter is incremented.

Figure 8: EE-SX-672-WR Mounted on Truck Hangers with Custom Encoder Disk The sensor detects when its beam is broken, meaning that a custom rotary encoder wheel with slots could be used with our truck’s skateboard wheels to count pulses corresponding to a twentieth of a rotation. These pulses are used every sixtieth of a second to generate ground speed, then the counter is refreshed for the next cycle. The mounted sensor can be seen in figure 8. Of note, the sensor is listed for a 1khz minimum top response frequency. We aimed to avoid exceeding this frequency, as we could not guarantee accurate functionality beyond this frequency. For this reason, we determined that twenty pulses per rotation would be a suitable choice. It results in our target 14

of 1kHz at 30mph, as seen in equation 1.

Given: 1. Wheel radius = .0425m 2. Mph to m/s ratio = .44 3. Max ground speed of 30mph 4. 20 pulses per rotation on custom encoder disk (30 ∗ .44) 20 ≈ 988(pulses per second) (2π ∗ 0.0425) EE-SX-672-WR VCC (Brown) LED (Pink) Output (Black) GND (Blue)

(1)

Teensy 4.1 5V (or direct to 4.5V battery) 5V (or direct to 4.5V battery) 38 (Pull Up Required in Code) Any GND

Table 1: EE-SX-672 Terminal Arrangement with Teensy 4.1 Connections According to the Terminal Arrangement available on the OMRON listing, the brown and pink wires both receive Vcc, while the blue wire is ground and the black wire is the signal output. This is important to take note of given that the black wire is the signal output. This can be seen in Table 1.

In order to track board orientation, an LSM6DSOX from Adafruit was used. It provides 3-axis gyro and accelerometer data via I2C on either 3.3V or 5V. It was an obvious choice due to its small size, price point, and ease of use. It is simply mounted next to the Teensy in its housing, and it must be level with the surface of the board as seen in the bottom left of Figure 7.

LSM6DSOX Vin GND SCL SDA

Teensy 4.1 Any 3.3V Any GND 19 (SCL Capable) 18 (SDA Capable)

Table 2: LSM6DSOX Arrangement with Teensy 4.1 Connetions The sensor used to measure hanger angle is the AS5600 Position Sensor from ams-OSRAM. It is a chip that is able to detect variations in a magnetic field generated by a small magnet attached to a rotary element. In our case, this was a small magnet epoxied to the back of the shaft of the motor used to rotate the truck hangers. The custom mount and magnet location can be seen in figure 9.

This sensor comes with the capability to run off of both 5V and 3.3V, which is convenient for our 3.3V Teensy’s usage. It can also output its readings either via i2c or a 12-bit DAC. Because we knew that we would be using at least two of these sensors, we chose to use the analog mode due to the potential headache of changing the i2c address of one or more sensors for concurrent use within our system. Such capabilities can be seen in figure 10, taken from the aforementioned ams-ORSRAM listing.

15

Figure 9: AS5600 Mounting System

Figure 10: AS5600 Block Diagram Our supplier for a PCB using this chip – accessible at this Amazon link from QCCAN – implemented a 3.3V specific board, and this is what we chose to use due to its inexpensive price point and ease of use with the Teensy. Delivering 3.3V is as easy as powering it from a 3.3V Vcc rail on the Teensy, and its analog output can be read with any of the analog-capable pins. Of note, the R4 resistor must be removed to enable analog output mode for this specific PCB. Given that Amazon listings can and likely will change in the future, any PCB implementing the AS5600 can likely be used. It is important to make sure a similar resistor pull-down is noted and addressed if present as with the PCB we used.

Datasheets for each sensor used in the truck design (and additionally the test rig) are located in the docs subdirectory of the delivered software repo, as seen in figure 11.

3.4

Truck Software

The software repository used to control our dynamic trucks will be delivered in a zip file to LSD. The repository’s general structure can be seen in figure 11. The code specific to the trucks is 16

within the system subdirectory.

Figure 11: Delivered Software The control algorithm is predominantly implemented in Arduino code, a language designed by Arduino software creators. It simplifies C/C++ capabilities, eliminating the need for setting up Makefiles and other complexities. Consequently, all truck code is executed as Arduino code.

Given the truck’s real-time response to clock-based and interrupt-based events, global variables and volatile flags are essential for data accessibility across multiple functions. Although a class-based system could prove beneficial for future development, time constraints, and multiple contributors hindered its implementation.

Despite the limited time, the code repository is well-documented and prepared for ongoing development and version control, making it an ideal foundation for advancing the technology’s software maturity. It encapsulates numerous lessons learned in embedded device software development.

Future developers should easily comprehend the code’s general structure by examining the provided repository, which offers ample opportunities for improvement.

3.5

Filtering and Control

To achieve precise turning radii considering speed and lean angle, we designed a control algorithm to manipulate the trucks using system data. The algorithm encompasses an extended Kalman filter, a dynamics function, and a feedback motor controller.

3.5.1

Extended Kalman Filter

At the beginning of every time step, the system collects data from all its sensors. The composition of these measurements can be seen in Equation 2 where ω is the rotation rate vector in the body frame, a is the gravitational acceleration vector in the body frame, v is the speed of the board, θ1 is the angle of the front truck, and θ2 is the angle of the rear truck.   ω a    y(k) = g(x(k)) =  (2) v θ1  θ2

17

In their raw state, these measurements only provide partial information needed for system control, and they are affected by noise due to uneven terrain. These factors prompted us to develop a filter that estimates the board’s orientation and smooths out noise from measurements.

More specifically, we developed an Extended Kalman Filter (EKF), a type of observer for systems with non-linear state transition and measurement equations. In this case, an EKF is required over a standard Kalman filter because attitude determination is a non-linear problem with non-linearities in both the state transition equation and the measurement equation. It achieves this by linearizing the system about the current state at each time step. We needed to define our state, which contains all the properties required to describe our system, namely the orientation and rotation rates of the system, along with speed, and the truck angles.

There are many possible choices of parameter sets to describe orientation, and our initial choice was 3-2-1 Euler Angles, also known as yaw, pitch, and roll angles. This set describes a rotation ψ about the z axis, a rotation θ about the y axis, and a rotation ϕ about the x axis. This set has the benefit of the roll angle ϕ equaling the tilt angle we need for the rest of our control algorithm.

However, as we found out in implementation, this parameter set has drawbacks. Looking at the state transition equations for 3-2-1 Euler Angles (Equation 3), we find these equations are highly nonlinear, with products of trigonometric terms. Additionally, there are singularities around θ = ±90◦ .

Although the board hopefully should never be in these orientations while riding, they could still cause issues if someone were carrying the board or leaning it up against the wall.      ψ̇ 0 sin ϕ cos ϕ ω1  θ̇  = 1  0   cos θ cos ϕ − cos θ sin ϕ ω2  cos θ cos θ sin θ sin ϕ sin θ cos ϕ ω3 ϕ̇

(3)

Because of these factors, in our final EKF, we ended up opting for quaternions, a 4-parameter set for representing orientations (β0 , β1 , β2 , β3 ) which are non-singular and have a much simpler state transition equation (Equation 4).    β0 −β1 −β2 −β3 0    1 β β −β β ω 1 0 3 2   1 β̇ =  (4)    β0 −β1 ω2  2 β2 β3 β3 −β2 β1 β0 ω3 Additionally, the tilt angle can easily be calculated using Equation 5, which removes any advantage that a 3-2-1 Euler Angle EKF holds over a quaternion-based filter.

2(β0 β1 + β2 β3 ) −1 ϕ = tan (5) β02 − β12 − β22 + β32 We can combine the quaternion orientation representation (β), rotation rates (ω), speed (v), and truck angles (θ1 , θ2 ) into the system state vector (x), which is shown in Equation 6.

T x = β0 β1 β2 β3 ω1 ω2 ω3 v θ1 θ2

(6)

Having established the state vector composition, the subsequent step involves determining the state transition and measurement equations of the system. The state transition equation’s form is evident in Equation 7. Since there are no expressions relating our state variables to the rate of change of v, θ1 , and θ2 , we have v̇ = θ˙1 = θ˙2 = 0. Consequently, all changes in these variables are assumed to result from external disturbances.

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  β̇ ω̇     ẋ = f (x) =  0 0 0

(7)

Equation 4 provides β̇, while the equations of motion for a rotating rigid body offer ω̇, as depicted in Equation 8. By assuming that the body frame aligns with the system’s principal axes, the calculation is considerably simplified, eliminating the need to invert the inertia tensor [I]. The precise values in our inertia tensor can be found in Appendix E.   (I3 − I2 )/I1 · ω2 ω3 ω̇ = [I]−1 ω × [I]ω = (I1 − I3 )/I2 · ω1 ω3  (8) (I2 − I1 )/I3 · ω1 ω2 Lastly, since the EKF operates at a constant timestep ∆t, it is necessary to discretize the state transition equation. With the EKF running at a high frequency of 240Hz, a first-order difference approximation suffices (Equation 9), negating the need for more computationally demanding methods like Runge-Kutta. By combining Equations 4, 7, 8, and 9, the state transition equation is obtained. x(k + 1) − x(k) (9) ∆t Subsequently, an expression depicting our system’s measurements is required. The general form of this expression is presented in Equation 2. However, a representation of a in terms of our state variables is needed. By converting the quaternion representation of the board’s orientation to the corresponding direction cosine matrix, we can multiply this by the normal force acceleration vector, which is 9.81 m/s2 in the inertial z direction. This yields the measured body frame acceleration, as demonstrated in Equation 10.    2 β0 + β12 − β22 − β32 2(β1 β2 + β0 β3 ) 2(β1 β3 − β0 β2 ) 0 2 2 2 2    2(β1 β2 − β0 β3 ) β0 − β1 + β2 − β3 2(β2 β3 + β0 β1) 0 (10) a= 2 2 2 2 2(β1 β3 + β0 β2 ) 2(β2 β3 − β0 β1 ) β0 − β1 − β2 + β3 g ẋ ≈

We now have the measurement equation for our EKF. Additionally, the EKF necessitates the process and measurement covariance matrices Q and R of the system. We derived the values for R using the square of the RMS error value from the IMU datasheet, assuming all off-diagonal terms of the covariance matrix were 0. The covariances of speed and angle measurements were unknown, and their values were determined through trial and error. Similarly, the process noise Q was unknown, and its values were established by trial and error. The matrices used in the EKF can be found in Appendix F. The EKF was initially implemented in MATLAB and tested on data collected using the test rig. Test runs were conducted on both smooth and bumpy surfaces, with the ultrasonic sensor on the platform serving as a verification method to ensure the EKF values corresponded with reality.

The results of these tests are displayed in Figures 12 and 13.

As can be seen, when the ground gets rougher, the performance of the EKF also goes down.

That said, the filter’s tracking error remains close to the true value regardless of the surface. With this result, we moved forward with implementing the EKF on the Teensy. Operating at a frequency of 240Hz, the board takes measurements and runs them through the EKF to estimate the board’s 19

Figure 12: EKF performance on smooth ground

Figure 13: EKF performance on rough ground

20

current state. With the filter implemented, we now have the tilt angle and board speed, which can be used to determine the desired turning radius using the system’s dynamics.

3.5.2

Optimal Lean Steer Physics

As we want our board to follow optimal lean steer physics, we must determine this ”optimal” relationship between velocity, tilt angle, and turning radius. We start by modeling the system as an inverted pendulum and creating a free-body diagram, which can be seen in Figure 14. Using

Figure 14: Free body diagram of the rider-board system in a turn this, we find the forces acting on the system in the x and y directions. ΣFx = −mac = −FN sin ϕ

(11)

ΣFy = 0 = FN cos ϕ − mg

(12)

Solving for the normal force FN in Equation 12, we then plug this into Equation 11. ac = g tan ϕ

(13)

Combining this with the equation for centripetal acceleration, we get v 2 = grCOM tan ϕ

(14)

The radius of the center of mass rCOM is related to the turning radius r by rCOM = r − h sin ϕ

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(15)

Finally, by combining Equations 14 and 15, we find that the following relation can describe optimal lean steer physics v2 r= + h sin ϕ (16) g tan ϕ Using the tilt angle and speed found above, we can use the optimal lean steer to calculate the desired turning radius for the current state. This turning radius can then be converted into the desired truck angle to achieve that turning radius, which can be seen in Equation 17.

ℓ −1 (17) θ = tan 2r 3.5.3

Feedback Motor Controller

Figure 15: Closed loop motor controller At every timestep, the filtered truck angles y(t) are compared with the reference inputs r(t) to calculate the error signal e(t). This error signal is then fed into the controller, which converts it to a direction and number of steps for the stepper motor. These steps are sent as control signals u(t) to the motors. The control loop updates at 60Hz, refreshing the signals sent to the motors with each timestep.

The controller is a straightforward proportional controller, multiplying the tracking error by a proportional gain (Kp ) to determine the number of steps sent to the motor. Although more advanced control architectures could have been employed (PD, PID, etc.), we chose a proportional controller for its simplicity. The added complexities of implementing a more advanced controller would yield minimal benefits. For instance, the actuation mechanism exhibits minimal friction, resulting in negligible steady-state error in the system, and thus an integrator term would offer little performance improvement. Furthermore, due to the small range of actuation and the high speed of our stepper motor, we could operate our controller with a relatively low proportional gain.

This eliminated overshoot of our reference input, reducing the advantage of adding a derivative term to our controller.

During testing, we found our controller performed well in two aspects. Firstly, for a given reference input, our system could track it with a relatively low tracking error (Figure 16). The slight tracking error can be attributed to system delays and the ramp-like nature of the reference input, which introduces a steady-state tracking error even for more advanced controllers like PI, PID, etc. This explains why the standard deviation of the 5 m/s run is higher than the 10 m/s run. The steeper ”ramps” result in increased steady-state error.

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Figure 16: Controller performance at various speeds Additionally, the system followed our analytically derived model, as shown in Figure 17. The hysteresis seen can again be attributed to the delay in the system as well as the ramp-like inputs given to the system.

3.6

Bench Top Testing

Our project wrapped up with the initial testing of our system. Although we had envisioned performing testing using our testing rig, we first started by performing testing on a tabletop. Our setup for this testing can be seen in Figure 18. We simulated the board moving at various speeds and tested the actuation mechanisms to see if they acted as expected. We found that the system was able to measure tilt angle accurately, and was able to drive the motors to the correct position.

This can be seen in Figure 17. We then proceeded to attempt to put weight on the board and found that the motors were not able to produce the torque necessary in order to actuate the trucks.

Because of this, it did not make sense to perform testing using our testing rig.

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Figure 17: Truck angle and tilt angle follow analytically derived relationship

Figure 18: Performing system testing at a simulated 5 m/s. As can be seen, the trucks can turn themselves when the sensor is tilting (simulating a turn)

4

Economic Analysis

Careful consideration of the economics of the project is necessary to ensure adequate planning for successful product introduction to the market. From our discussions with LSD LLC, we understand that the product will be marketed as a truck-mountable solution that can be attached to existing boards. There may also be the option to create complete LSD boards with the mountable solution already installed. The purpose of this section is to discuss the economics involved with the project and how it aligns with the sponsor’s long-term goals.

To begin with, let us consider the following, which is the total cost of manufacturing the entire 24

truck in ENGS 89 and 90.

Figure 19: ENGS 89/90 BOM list including the costs of the various materials that went into manufacturing Admittedly, the total cost arrived at is quite high. However, it is important to note that the cost figures listed above are for the raw products that were custom milled in the machine shop. The hours were calculated based on the time it took us at our experience level to make the parts. With manufacturing processes like injection molding (for more basic parts) and metallic 3-D printing (for more complicated parts like the tulip), we project that the labor costs, which currently constitute a major part of our incurred costs, will be reduced significantly. We, thus, expect the market-ready per-truck cost total price to be lower than that stated above if LSD streamlines the manufacturing process and supply chain to cut costs.

As observed in the two graphs above, there has been an uptrend in the value of the skateboard market in the US. Likewise, the number of skateboard users in the past decade has remained relatively stable, with a recent uptick in riders in the past two years. This shows that there is an available and growing market that LSD can tap into.

Consequently, a sound pro forma understanding of the financial requirements for large-scale, long-term implementation of the desired product is necessary for successful market penetration.

Our analysis involved various assumptions that took several factors like the costs of development, 25

(a) Uptrend of the skateboard market value

(b) Uptrend of the skateboard users

Figure 20: Trends in skateboard market production, and expansion into account. We calculated a net present value (NPV) of approximately $2 million over a four-year period, indicating a potentially viable business model for our product.

The NPV is a financial metric used to determine the current value of expected future cash flows, adjusted for the time value of money. This means that we are able to evaluate the profitability of our product by accounting for the fact that money received in the future is worth less than money received today due to inflation and the opportunity cost of not having access to that money now.

We have conducted a thorough analysis of the values and factors that contributed to the NPV calculation, which are presented in Appendix G. While our initial project output is modest, producing only 250 samples per year, we have targeted a niche higher-end market segment. We have kept our projections conservative, but if the actual financial results meet or exceed our expectations, our future year projections will be cash-flow positive and contribute to the NPV. We anticipate an initial investment of about $800 thousand in startup capital to fund product development, launch, and raw material procurement to support production in case of revenue order delays. The costper-two-trucks is projected to be $1000. This is a reasonable estimate based on our projected calculations for a streamlined manufacturing process. Our break-even point is projected to occur within the first two to three years of operation, after which we expect to be fully cash-flow positive.

By year three, we should be able to sustain growth and scale up our production concurrently.

Our financial analysis indicates a promising business outlook for our product. We have taken a cautious approach to our projections. Still, with an initial investment of $800 thousand and a focus on our targeted market segment, we anticipate a successful launch and a profitable future.

5

Recommendations for Future Work

5.1

Test Rig

Our biggest suggestions for improving the functionality of the test rig are as follows. Currently the mechanism for mounting the surgical tubing works, but an exploration of other techniques is recommended. Either redesigning the attachment point and interaction, or fully moving away from surgical tubing may be viable options. Additionally, the current placement of the pully is a little lower than ideal. This results in the bail rope rubbing on the main truck fork increasing friction and making it harder to lift Jerry. Changing the height of the pulley or the location should be explored options.

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5.2

Mechanical

General advice for improved quality of life of the current aluminum truck design includes reducing friction generally. Strategies include adding lithium grease in areas of aluminum-aluminum rubbing and thrust bearings or oily bronze washers in places that explicitly need extended lubrication.

5.2.1

Return to Center Mechanism

We feel that developing this RTC further would be time well spent. The relative simplicity and effectiveness of the design allow much more room for expansion of the other mechanisms to spaces closer to the board–increasing the tilt range. The main problems with the RTC can be separated into two main parts. First, the preloading, or tightening of the truck, allows for a stiffer RTC. This would be equivalent to tightening the bushings on a standard truck. Second, guiding the Tulip on the shaft and preventing rotation.

Preloading: Preloading is an essential part of customizing a skateboard to user preference. At the moment, the only method of customization is shimming the RTC before mounting it and this was usually the most dreaded part of assembling the truck. However, stiffer trucks usually resulted in a better feel. We have curated two potential options for creating and tightening the new RTC: The first: creating a custom shaft collar that expands. The shaft collar would work similarly to a Lab Lift. The collar would sit on the shaft behind the urethane and would expand and contract subject to the single bolt running out of its side.

The second: A pseudo-kingpin. This would be a sleeve that fits over the shaft holding the Tulip. This sleeve would be behind the urethane with an ID similar to the shaft and an OD just under 3/4”. This pin would have a threaded OD that threads into the baseplate and tilts with the board while freely spinning relative to the hanger box. The head of the pin would have flats that fit into the slot to keep it locked in place. This is an adaptation of the Original Trucks’ design that implements a similar technique to tighten the spring. Please note that removing the electrical system with the suggested implementation would need to be reworked such that the hanger rotates appropriately to the board’s tilt. For purely mechanical trucks that use the revised RTC, reverse engineering the Original Trucks mechanism to work with the cams from LSD’s TruckV3 is needed.

Double-D Shaft Alternatives: The double D shaft holds a lot of torque and is currently made from stainless steel to combat this. However, alternatives should be looked into as they may help reduce the deformation that results from max leaning and full torque on the aluminum.

Heavy-duty splined shafts may provide a good alternative. They are an extension of the design provided by Helix Design with added slots and will usually come with tight-tolerance followers that have mounting holes that the Tulip can be secured to. Modifying the ends of the shafts to larger or smaller diameters, both threaded and not threaded, would provide versatility to different applications in future designs. Another alternative is preventing the Tulip’s rotation by securing it to the hanger box. Options include directly pinning the tulip into a slot in the hanger box or extending the bottom and adding a large flat that interacts with the top of the hanger box and can freely slide forward and backward while preventing rotation. These alternative securing methods eliminate the need for a double D shaft and mitigate the concern of developing backlash from deformation. However, the suggested points where the Tulip interacts with the hanger box are currently exposed and excess debris could result in galling or the mechanism failing.

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5.2.2

Hanger Actuation

Hanger actuation is one of the most difficult problems to solve in developing any sort of dynamically controlled truck. Any implementation must remain extremely robust while also responsive.

Although we were able to implement hanger rotation with a cam profile that contacts two roller bearings, it induced several problems, as listed below.

1. The cam profiles are difficult to design, machine, and maintain.

2. There was a significant amount of backlash present. It is difficult to perfectly engage the cam profile up against the roller bearings without having any backlash present.

3. Torque transfer is not ideal due to a high degree of friction being present. Significant grinding was present on both the tulip and hanger cam.

4. The cam takes up a relatively large amount of space, which proved particularly difficult to work with given the hanger box’s sizing needs to have sufficient ground clearance.

For these reasons, we recommend pivoting away from a cam-based actuation system to another system. This could be like a bevel gear system with a motor mounted in a similar location but with a high-reduction gearbox. Overall, more time could be spent testing a robust actuation mechanism that is also fast and accurate.

It also may prove beneficial to move away from stepper motors and implement a design using a more powerful motor. Stepper motors are great for high positional accuracy, but high torque is needed to maintain hanger angle. A servo motor or a normal DC motor with an encoder may prove more effective at changing the hanger angle under load.

Additionally, it may be necessary to introduce a gearbox to the design to achieve the level of torque needed to turn the hangers. A potential low-profile option for this is a planetary gearbox due to its high reductions with minimal reduction stages.

5.3

Electrical

With both the test rig and system electrical design, all the sensors are selected to be durable in rough environments, but they are still prone to failure. One way electrical failures can be avoided is to add redundant sensors. This would allow for fault detection and prevent single points of failure.

Additionally, our electrical boards are soldered on a perforated breadboard. While this is fine for prototyping, it can come undone more easily than a PCB design and takes much longer to manufacture. Therefore, it may be more advantageous to have a PCB for a better, more secure circuit board.

5.3.1

One Battery with Voltage Conversion

Currently, our power sources are separated into a 4.5V battery (3S AA batteries) and an 18V battery (2S 9V batteries). However, we can redesign using only one voltage source with appropriate voltage regulators. For a solution without the integrated skateboard batteries, we can use an 18V battery with buck converters that drop the voltage to 4.5V to safely power Teensy 4.1 and other sensors while allowing the 18V source to drive the motors. For a solution on an electric skateboard, a ladder configuration of voltage droppers (to 18V and to 4.5V) may be required as the electric skateboard batteries are usually much higher voltage than 18V. Additionally, when selecting buck converters, it would be wise to have them be automotivegrade so they can be shielded from nearby high-frequency switching caused by the Teensy 4.1 or any MCU. 28

5.4

Controls

Recommended improvements to the control system include modifying the Extended Kalman Filter to include centripetal acceleration and developing a more advanced motor controller for improved performance.

5.4.1

Extended Kalman Filter Improvements

As discussed in Section 3.5.1, our sensor uses the measured gravitational acceleration vector as one of the measurements to determine the lean angle of our system. In a static environment or when moving at low speeds, this is a reasonable approximation. However, as speed increases, other accelerations are experienced by the board, most notably centripetal acceleration. To account for this, one would have to modify the acceleration equation to include these effects. The centripetal acceleration vector would have a magnitude of v 2 /r and would be pointing to the center of the turn (Figure 21). The speed of the board is measured, and the turning radius can be derived through inverting Equation 17 and using the angles of the trucks.

Figure 21: Centripetal acceleration experienced by the system. Acceleration is not in the body frame or inertial frame, so a new frame is needed. The transformation from prime to body frame is a roll about the x-axis by the tilt angle ϕ.

Because this vector is neither in the inertial nor body frame, one would need to perform the proper transformation (rotation of ϕ about the x-axis) to describe the acceleration in body frame coordinates. This updated form of the acceleration measurement equations can be seen in Equation 18, where ag is the gravitational acceleration described in Equation 10.    1 0 0 0 a = ag + 0 cos ϕ − sin ϕ v 2 /r (18) 0 sin ϕ cos ϕ 0 While this does increase the complexity of implementing the EKF, it could lead to increases in filter performance, especially in high-speed dynamic environments.

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5.4.2

Motor Controller Improvements

Currently, the system uses a simple proportional controller to convert the truck angle error signal to motor control signals. We intentionally implemented a simple controller as it would require less time to get working, and we felt that the performance tradeoffs were worth it for this initial prototype. Additionally, because we used stepper motors, the signals we sent to the motor were the number of steps to take. We could not affect the speed of the steps, meaning that adding more advanced motor controllers would not have made sense for our choice of motor. As we highlighted in Section 5.2.2, stepper motors are not the best choice for this project. Instead, something like a servo motor or DC motor should be used as they offer significantly more torque.

These motors, however, require more advanced control schemes, meaning that future teams would have to implement a PD or PID motor controller to get the desired performance out of the motors.

5.5

Potential Future 89/ 90 Projects

We believe that there are a couple of avenues for future ENGS 89/ 90 projects that continue the work we have done. They are a complete redesign of the trucks and the creation of a more sophisticated electronics system.

5.5.1

Trucks

One of the main focuses of our project was the creation of skateboard trucks that achieve 3 main objectives: decoupling leaning and steering, allowing for larger tilt ranges, and electronic actuation of the skateboard truck. However, because our project had so many different tasks, we could not dedicate enough time to create a fully fleshed-out, sleek design. An ENGS 89/90 group could be tasked with overhauling the mechanical design of the trucks. This would entail design for manufacture, as well as the development of a novel actuation method that can provide the high torques necessary while remaining responsive and robust damages caused by sand and water on the road. This project would be mostly mechanical in nature, however, a cursory knowledge of control theory would be beneficial as motor controllers may be needed depending on the group’s motor selection.

5.5.2

Electronics

The other main focus of our project involved the creation of an electrical system that handled sensing data from the system and processing that data. As this was the main focus of the project, aspects such as powering the system and PCB design were neglected. A group could be tasked with updating the electrical system to use a large battery with voltage conversion for motors and sensors, use redundant sensors with fault detection algorithms to increase the robustness of the system, and create PCB designs to better house all of the electrical components of the system.

A team for this project would consist of mostly Electrical Engineers and Computer Scientists/ Computer Engineers.

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A

References

References [1]

J. Fox, Damping system for skateboards, en, Jun. 2014. [Online]. Available: https://patents. google.com/patent/US8752849B1/en?q=speed+wobble+skateboards&oq=speed+wobble+ skateboards.

[2]

M. Burrows, C. Burd, and B. McKenzie, “Commuting by Public Transportation in the United States: 2019,” en, p. 11, [Online]. Available: https : / / www . census . gov / content / dam / Census/library/publications/2021/acs/acs-48.pdf.

[3]

D. Rajewski, Turn vs. lean: Dialing in the perfect longboard set-up, en, 2017. [Online]. Available: https://stokedrideshop.com/blogs/stoked-school/turn-vs-lean-dialing-in-theperfect-longboard-set-up.

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B

Figures in Report

List of Figures 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28

First Mile Last Mile Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Solidworks of testing rig . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Test Rig Housing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Components of LSD’s original mechanical truck . . . . . . . . . . . . . . . . . . . . .

Redesigned return to center . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Prototype design of trucks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Teensy with Gyro and Motor Controllers . . . . . . . . . . . . . . . . . . . . . . . . .

EE-SX-672-WR Mounted on Truck Hangers with Custom Encoder Disk . . . . . . .

AS5600 Mounting System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

AS5600 Block Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Delivered Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

EKF performance on smooth ground . . . . . . . . . . . . . . . . . . . . . . . . . . .

EKF performance on rough ground . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Free body diagram of the rider-board system in a turn . . . . . . . . . . . . . . . . .

Closed loop motor controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Controller performance at various speeds . . . . . . . . . . . . . . . . . . . . . . . . .

Truck angle and tilt angle follow analytically derived relationship . . . . . . . . . . .

Benchtop testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

BOM for Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Trends in skateboard market . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Centripetal acceleration of rider . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Baseplate angle description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Initial tulip prototype for torque verification . . . . . . . . . . . . . . . . . . . . . . .

Baseplate FEA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Hanger FEA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Aluminum Truck . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

System and Test-Rig Block Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . .

NPV calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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7 10 10 11 12 13 14 14 16 16 17 20 20 21 22 23 24 24 25 26 29 33 34 35 35 36 37 40

C

Additional Figures

C.1

Baseplate Angle

Figure 22: Baseplate Angle θ is the angle of the hanger, holding the wheels, relative to the board [3].

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C.2

Tulip Prototype for Torque Verification

(a)

(b)

(c) Turning load

Figure 23: Initial Tulip prototype for torque verification(a). The bottom view (b) provides a view of the wrench flats used keep the tulip from rotating, and (c) is the machine brass follower with a hex on the back for wrench access. We measured the torque produces by this RTC to peak at 29.5 oz-in with no initial compression (preloading) of the urethane. .

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C.3

FEA of Truck Design

(a) Static load

(b) Turning load

Figure 24: FEA of baseplate undergoing various loading conditions. As can be seen, even in the worst possible situation, the part has a safety factor of 2. In reality, it is likely higher, as all of the rider’s weight will not be supported by one truck .

(a) Static load

(b) Turning load

Figure 25: FEA of hanger box undergoing various loading conditions. As can be seen, even in the worst possible situation, the part has a safety factor of 2. In reality, it is likely higher, as all of the rider’s weight will not be supported by one truck.

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C.4

Aluminum Truck

(a)

(b)

Figure 26: Close up photographs of the fabricated aluminum prototype truck.

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C.5

Block Diagram for Code of Both Systems

Figure 27: System and Test-Rig Block Diagram

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D

Tables in Report

List of Tables 1 2

EE-SX-672 Terminal Arrangement with Teensy 4.1 Connections . . . . . . . . . . . . 15 LSM6DSOX Arrangement with Teensy 4.1 Connetions . . . . . . . . . . . . . . . . . 15

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E

Moment of Ineria   103.49 0 0 103.52 0  kg m2 [I] =  0 0 0 0.5

F

Parameters for Extended Kalman Filter Q = 10−8 · I10×10

  0.001042 0 0 0 0 0 0 0 0  0 0.001042 0 0 0 0 0 0 0    2   0 0 0.00104 0 0 0 0 0 0   2  0 0 0 0.02354 0 0 0 0 0    0 0 0 0 0.023542 0 0 0 0  R=    0 0 0 0 0 0.023542 0 0 0    2   0 0 0 0 0 0 0.001 0 0   2  0 0 0 0 0 0 0 0.001 0  0 0 0 0 0 0 0 0 0.0012 P0 = Q

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40

Net Present Value Analysis

Figure 28: With an initial projected investment of $800 000, the Net Present Value Calculation for Project, the NPV is approximately $2 million over a 4-year period

G

H

Testing Rig Documentation

41

Testing Rig Technical Documentation Group 6

March 14, 2023

Contents 1

Summary

2

2 Contents

2

3 Introduction

4

4 Instructions

4

5 Conclusions

5

6 Acknowledgement

5

1

1 Summary The testing rig aims to measure the inputs needed to modulate the steering response of the board to balance gravitational lean inward forces with outward centrifugal forces, even without rider intent. This modulation is achieved by creating speed-dependent corrections to turning radii, which will modulate the wave frequency so that the oscillations do not happen too fast for a rider to react quickly enough to get the board out of "free-float" mode and into "rider intent" mode. The testing rig is equipped to measure ground speed, tilt angle. By recording all of the measurements in real-time using an on-board SD card, the testing rig generates the correct inputs for the product.

2

Contents

The testing rig includes a board with a "human-like weighting system" present on top, a secure "ankle" attached to the board, and elastic tubing with a 3D printed attachment to keep the "human" centered between the "forks" of the board. Additionally, the testing rig has an on-board gyro to measure speed and tilt angle.

Figure 1: Testing Rig 2

Figure 2: Fork

Figure 3: Surgical Tubing

3

Figure 4: Ankle

3 Introduction The testing rig described in this technical documentation serves a critical purpose in ensuring the safety and efficacy of a new skateboard design. This rig allows the team to test the board’s performance at high speeds with a human-like weighting system present on top. The goal is to verify that the board can maintain a general straight path, even with oscillation, and achieve appropriate hanger angles for a smoother ride. The testing rig is designed to measure ground speed, tilt angle using an on-board gyro, and produce the inputs necessary to adjust the appropriate resultant turning radii from the stepper motors. Ultimately, the testing rig ensures that the board is safe and ready for human riders.

4

Instructions

The instructions on testing rig are: 1. Mount the testing rig securely onto the skateboard using the attachment hardware provided. Ensure that the rig is centered and balanced on the board.

2. Connect the fork to the tow hitch and adjust its height according to the height of the applied weights on testing rig.

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3. Mount applicable weights to the testing rig.

4. Set up the surgical tubing with the 3D printed attachment so that it centers the "human" on the board and secures the ankle to the board.

5. Connect the testing rig to a power source, such as a battery, and turn it on. The gyro is recording all measurements in real-time using the on-board SD card including the ground speed and tilt angle.

6. Begin testing by driving the truck at increasing speed. The testing rig should stay in a general straight path behind the truck. Some side to side oscillation will likely occur.

7. Raise the pulley in case the testing rig begins to lean beyond oscillation and to bring it to a halt at the end of the testing rig.

8. Repeat the testing as necessary to ensure riding behavior at different weights and speeds. The inputs of the behavior is recorded in SD card.

Note: It is important to wear appropriate safety gear, such as a helmet and pads, when testing the skateboard. Additionally, always test the board in a safe and controlled environment to prevent accidents or injuries.

5

Conclusions

In conclusion, the testing rig described in this technical documentation is a crucial tool in ensuring the safety and performance of a new skateboard design. By measuring ground speed, tilt angle, and producing the necessary inputs to adjust the turning radii, the rig ensures that the board can balance gravitational lean inward forces with outward centrifugal forces, even without rider intent. The testing rig is equipped with a "human-like weighting system," an on-board gyro, and a secure ankle attachment to keep the "human" centered between the "forks" of the board. By following the provided instructions, the testing rig can be mounted securely onto the skateboard and tested at various speeds and weights to ensure safe and effective riding behavior. Overall, the testing rig is an essential component of the product development process for this new skateboard design.

6

Acknowledgement

We want to acknowledge the Transportation Services for providing testing parking location.

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