Kinematic Laser Mount ME 324: Precision Engineering
Bethany Chaffin, Ian Sparkman, Jamie Young, Keven Wang 8 May, 2018
Background & Purpose The goal of this project was to design and manufacture a kinematic mount for a small laser that would allow for calibration of one axis of rotation of the laser. Additionally, the mount was required to function such that the laser could be removed and reattached while maintaining its original orientation with little to no re-calibration. Designing a kinematic mount allows one body to be located with respect to another with high repeatability while constraining the body to a desired set of degrees of freedom. In this case, the laser needed to be constrained in all degrees of freedom except for one axis of rotation. Moreover, using a laser as the object for the kinematic mount provided a built-in measurement tool for determining the resolution, range, dynamic range, and repeatability of the mount. These characteristics were able to be measured at multiple distances from the mount. The laser was not perfectly collimated (as will be discussed in later sections), resulting in larger points of light at further distances from the source, but still allowed for repeatable measurements.
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Design & Fabrication In order to simplify the design and reduce the number of parts in the kinematic laser mount, a two-plate design was employed. The mount consists of a back plate that can be clamped to any heavy base, and a front plate that accepts the laser. The two plates were mounted together using a modified Kelvin clamp-type method: the rear plate has a cone (as an approximation for a trihedral pocket), a vee groove, and a flat surface machined to accept, respectively, two steel spheres and a ball-end screw attached to the front plate. Larger magnets embedded in each plate allow simple repeatable reattachment of the front plate without additional contact points between the two plates. A fine threaded ball-end screw (pitch = 80 threads / inch) was used to adjust the angle of the front plate with respect to the back. The ball-end screw made contact with the flat surface of the back plate and was positioned so that this contact point was at the same z-height as the laser. By positioning the ball-end screw’s contact point in this way, the relative movement of the front plate was limited to rotation about the vertical axis formed by the other two spheres, indicated in Figure 2.
Figure 2: Front plate with axis of rotation resulting from ball-end screw adjustment shown in red. The ball-end screw was threaded into an insert pressed in the leftmost hole. In order to retain the two plates, magnets are used. In particular, three magnets are inserted into holes along the pivot axis (see axis in Figure 2). The designed clearance between two opposite magnets was 25 thousandths of an inch (0.635 mm), allowing the magnets to be remain close and form a strong magnetic retaining force despite the rotation of the two plates. Also note smaller magnets were used to retain the two gage spheres in the machined cones. 3
In order to constrain the laser within the square hole, the front plate was designed with a notch and threaded hole for a set screw. This screw contacted the laser from above and secured it against two lines of contact from below from the angled walls of the square hole. When tightened by hand, the set screw held the laser in place securely enough that removing and reattaching the front plate did not affect the laser’s orientation. CAD of the connection can be seen in Figure 3 below.
Figure 3: CAD showing front plate, back plate, and the connection between the two
Fabrication To create the parts of the laser mount, aluminum stock was machined on a HAAS VF1 CNC mill. On the back plate, a shell mill was used to create a reasonably flat starting surface, and an oversized central bore ensures no contact with the laser while the front plate is mounted. The shallow cone-shaped pocket was created with a ball end mill using a spiral tool path that left cusps 2.5um in height, which we deemed an acceptably smooth surface for the purposes of this mount. The vee groove was machined using a 90° chamfer mill and a trace operation at increasing depths of cut, with a light finishing pass to ensure a satisfactory surface finish. The initial facing operation provided the flat surface for the ball screw. More magnet holes than necessary were machined in a triangular pattern that allowed for flexibility in initial assembly and testing. 4
The front plate was similarly faced and magnet holes were machined in a mirrored pattern from the back plate. The square pocket was machined with a light finishing pass using a full depth of cut to ensure a uniform surface for the laser to rest in. Shallow cones to constrain the two steel spheres were machined identically to the cone on the back plate, but with additional magnet holes machined further into the cone centers to retain the spheres. A bore was machined to allow a light press fit for a threaded insert to accept the ball-end screw. The front plate was then flipped and faced to a more desirable thickness, reducing its mass and potential to sag when mounted to the rear plate. Lastly, on the drill press, a hole was drilled and tapped to accept a set screw to constrain the laser in the square pocket. With magnets fixed into their respective holes with CA glue, the two steel spheres and the fine-pitch ball-end screw may be attached to the front plate as seen in ​Figure 4​, and the front plate may then be attached to the back plate for testing.
Figure 4: ​Finished back plate (shown on the left) and front plate (shown on the right)
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Experimental Procedure After the kinematic mount was manufactured and assembled, its range, resolution, and repeatability were measured and its resulting dynamic range calculated. Before measurements were taken, the kinematic mount was clamped onto a right-angle block, which was clamped onto a table. In order to measure the above characteristics, the laser was pointed at a surface, adjusted by a controlled angle, and the translations between laser dots on the surface were measured. The distance between laser to surface, the lever, was maximized in order to magnify the error. The table was carefully positioned and its sturdiness was verified by gently shaking the table. A duron board was placed at the opposite side of PRL to collect and measure the laser’s points of light. The duron board offered a long enough surface to capture the entire range of the kinematic mount at the maximum distance provided by the room. The distance between laser tip and board is measured with a tape measure. A general setup can be seen in Figure 5 below. Resolution The resolution of the kinematic mount was determined by positioning a duron board at a known distance from the laser’s source, marking the starting location on the board, and then rotating the ball-end screw by a known angle (90 degrees), resulting in a horizontal translation of the laser’s point of light on the board. The top (visible) end of the ball-end screw was marked with a dot so that it was easy to control the rotation of the screw to one revolution or a fraction of a revolution. Thus, the resolution of this kinematic mount relates the degree of rotation of the ball-end screw to the corresponding horizontal translation of the laser’s light at a known distance. Range The range of the kinematic mount was measured by positioning a long piece of duron at a known distance from the laser’s source, then rotating the ball-end screw from one extreme to the other in order to generate the maximum relative rotation of the front plate while maintaining contact of all three spheres with the back plate. Repeatability In order to measure the repeatability of the kinematic mount, a duron board was positioned at a known distance from the laser’s source, and the laser’s starting position was marked on the board. The front plate was then decoupled from the back plate and then put back 6
in its original position. The resulting position of the laser’s point of light on the board was again marked, and the distance between the two was measured. However, as will be discussed below in the Results section, there was no perceptible shift in the laser’s position on the board after decoupling and recoupling the front plate from the back plate. Dynamic Range The dynamic range was obtained by dividing the range by the resolution of the kinematic mount.
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Figure 5​: Measurement setup with laser clamped to table and duron at far end of PRL Results Both a short range and a long range trial were performed. For the short range trial, the laser and board were placed 4.78 meters apart, and for the long range trial they were 14.65 meters apart. Resolution With regards to the mount, the minimal repeatable motion was determined to be a quarter turn of the fine adjustment screw (i.e. 90 degrees). The corresponding displacement of the laser on the board was 4.80 mm for the short trial, and 14.75 mm for the long trial. This corresponds to ranges of 0.0575 degrees and 0.0577 degrees for the trial respectively, with an the average range across the two experiments being 0.0576 degrees. Range Moving between rotational extremes of the kinematic mount resulted in a maximum displacement on the board of 0.619 m for the short trial and 1.893 m for the long trial. This corresponds to angular ranges of 7.38 degrees and 7.36 degrees respectively, with an average range across the two experiments of 7.37 degrees. Repeatability When unmounting and remounting the front plate of the kinematic mount, there was no perceptible displacement of the laser on the whiteboard for either the short or long trial. Dynamic Range Calculated as range divided by resolution, the dynamic range of the kinematic mount was calculated as 128.2 for the short trial and 127.6 for the long trial, with an average across the two experiments of 127.9.
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Error Analysis The following factors presented potential errors in our measurements: ● Softness of Aluminum: Although aluminum allows for uniform expansion due to its good thermal conductivity, its relative softness results in deformation across repeated contact. Since the kinematic mount relies on point-to-surface contacts (ball to Vee, ball to surface) and point-to-line contacts (ball to cone), any slight variation in the geometry can result in significant displacement. During our two consecutive experiments, we did not observe noticeable difference caused by the deformation of aluminum. However, we are able to visually notice the scratches on aluminum at contact locations. This was especially true at the contact of the back plate surface and the fine adjustment ball screw. As such, we would also expect the accuracy and repeatability to degrade overtime after continuous usage. ● Repeatability of Ball Screw: The repeatability of adjusting the front plate’s orientation relied on visually verifying the rotation of the ball-end screw. For the purposes of this experiment, the manual adjustment of the ball-end screw was sufficient to produce repeatable measurements for resolution (as discussed above), but in the future if this setup were to be improved, it would be important to standardize the angle adjustment of the ball-end screw to ensure consistent behavior of the front plate across trials. ● Size of Laser Mark on Surface: Another source of error in the above measurements was the increasing size of the laser’s mark on surfaces at large distances away from the source. When measuring the delta between two points on the duron surface resulting from an adjustment of the ball-end screw, the starting and ending location of the laser had to be visually estimated as the center of the laser’s circle of light. Additionally, when measuring repeatability, this non-discrete circle of light made it impossible to notice any change in position when removing and remounting the laser from the back plate. This source of error was mitigated by being consistent in marking the laser’s location on each surface (e.g., using the same operator and the same pen in each trial), but if this experiment were to be redone with higher fidelity, it would be crucial to use a laser that was better collimated to reduce this uncertainty. ● Human Perception and Measurement: The accuracy of data collecting in this trial was limited to the resolution of the measuring devices used. For instance, the range of the laser was measured by marking two incidents on a whiteboard and measuring the distance between with a yardstick (resolution 1mm). Furthermore, repeatability was measured by marking a laser incidence, removing and replacing the front plate of the mount, and measuring any noticeable difference, of which there was none.
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Conclusions The repeatability of the kinematic mount between trials was astonishing. It was enlightening to witness the effect of an “exactly constrained” system at work. This repeatability seemed to justify the broader design methodology, described below: ● Minimize (Moving) Parts: By clamping to a 90 degree gage black, the kinematic mount needed just two simple machined parts, only one of which is moving [Front Plate]. Furthermore, it required a minimum of purchased components -- a fine adjustment screw, a threaded insert for said screw, two gage spheres, a ball-end set screw, and disk magnets -- all of which had guaranteed tight tolerances. This simplified mechanism was used in an attempt to eliminate mounting error from mechanical components, such as backlash. ● Magnetic Retaining Force: The use of magnetic force to couple the two components allowed us to use a simplified two plate design mounted to a 90 degree gage block. It also guaranteed consistent and easy connection without additional physical contact, leading to repeatability comparable or even superior to what could have been achieved using gravity as a retaining force. ● Equilateral Triangle: An equilateral triangle between the three zones of contact (cone, vee groove, and surface) was utilized. This was chosen because an equilateral orientation maximized stability, and the usable space between points. This was facilitated as there were no space concern, generally the major geometric constraint. Still, as discussed in the Error Analysis section, there was avoidable error in the system. For future iterations, this error would be addressed by improving the design in the following ways. ● Rotational Control of Adjustment Screw: For this trial, a quarter-turn of the adjustment screw was used as a minimum reproducible adjustment. However, this quarter turn was performed by hand using the human eye to resolve the rotational distance. To avoid this inbuilt error, two solutions could be adopted. First, a better rotational resolution scale could be added to the adjustment screw, giving the user a clearer idea of how far a true quarter turn is. A second and more robust solution would be to attach a stepper motor to control the adjustment screw, eliminating both sources of error discussed in this trial as well as decreasing the minimum reproducible adjustment. ● Rigid Material: Stainless Steel, as opposed to aluminum would be used to avoid the deformation previously discussed. This would greatly improve repeatability between trials and over long periods of time. This would introduce a much heavier system, however this could be alleviated by using stainless steel inserts for only the contact points between the two plates. 10
● Better Laser: A laser with better collimation would provide better resolution for relative movement of the laser within and between trials. ● Longer Test: By increasing the distance between the laser and the reflecting surface, movements of the laser within and between trials would result in larger displacements of on the reflecting surface, allowing for better resolution and repeatability measurements. This is especially relevant for the repeatability measurements, as no noticeable displacement was perceived between trials in this experiment. Practically, this longer distance could be achieved by using precision reflectors to route the laser a long distance in a small space. Note a better laser would be compliment the efficacy of a longer test. ● Better Experimental Setup: Fundamentally, the measurements in this trial were limited by their reliance on hand measurement and the perception of the human eye. Ideally, the human factor would be eliminated from data collection as much as possible because its resolution is inferior to that of a precision machine. It is unclear how this would be achieved, but it would likely involve a technology that could sense lasers and calculate distance between relative incidents. ● Better range: the range of our kinematic mount is measured to be 7.37 degrees. This is a rather small range. One cause is due to the two aluminum plates colliding into each other on both ends of the range. We could potentially increase this range by designing the geometry differently. Another limitation factor is the diminishing magnetic force as a function of distance. As the aluminum plate rotates further apart from the other plate, the magnetic retaining force was not enough to hold the aluminum plate in place. We could experiment with other forms of retaining forces such as gravity and springs.
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APPENDIX Experiment Data Experiment 1
Experiment 2
Average
Distance (cm)
478
1465
Range (cm)
61.9
189.3
7.378620655
7.362678955
Range (degree)
Distance (cm)
478
478
1465
Resolution full turn (cm)
1.92
1.97
5.9
Resolution quarter turn (cm)
0.48
0.4925
1.475
Resolution quarter turn (degree)
0.05753549147
0.05903381051
0.05768685749
Distance (cm) Repeatability (cm)
Dynamic Range
478
1465
0
0
128.2446794
124.9897405
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127.6318259
7.370649805
0.05761117448
127.9382527