Analysis of a Vise-Grip Charles Hunter AME40423 Mechanisms and Machines September 22, 2010 Abstract The purpose of this project was to analyze the tool know as a vise-grip. A skeleton diagram was developed and the degrees of freedom, F, and mobility, M, numbers were calculated using Grueblerâ€™s Criterion. A force analysis of the system was performed in order to determine how and why clamping occurs.

1 Engineering Analysis There is only one equation required to analyze the vise-grip in order to determine the degrees of freedom. Grueblerâ€™s Criterion to compute the degrees of freedom is, (

)

( )

(1)

where N is the number of links, P1 is the number of P1 contacts (joints which allow 1 degrees of freedom of relative motion between connected bodies), and P2 is the number of P2 contacts (joints which allow 2 degrees of freedom of relative motion between connected bodies) on the mechanism.

The mobility of the vise-grip cannot be found using an equation. The analysis for the mobility was found through observation. The mobility number is equal to the minimum number of links which need to be grounded in order for the mechanism to be considered a structure. In order to explain how the vise-grip â€œclampsâ€? onto objects a free body diagram was developed equilibrium equations were analyzed. Also equations for a four-bar mechanism whose coupler is driven by force were re-derived.

2 Results 2.1 Skeleton Diagram The vise-grip is a tool consisting of four links. The skeleton diagram of the tool shows a four-bar kinematic chain (Figure 1). The input link is the coupler, which is also the shortest. The overall mechanism is a rocker-rocker. In the diagram, N is 4 and P1 is also 4. An assumption was made when determining the number of P1 contacts. Link D is not a pin joint, it is actually two planer tips that contact each other at the end of the screw. Therefore the P1 contact is two P2 contacts. This does not affect the calculations of F or M and the mechanism is still considered a four-bar because one P1 contact is equivalent to two P2 contacts. Plugging these values into equation 1 gives a degrees of freedom, F, value of 1. By inspection, the vise-grip has a M value of 1 as well.

Figure 1: Skeleton Diagram of Vise-Grip Mechanism

The force, F, acting normal to the extension of Input 3 at a distance, L, produces a torque, T2, counterclockwise about link A. The angle between link 2 and link 3 is Ď•, and the angle between link 3 and link 4 is Îź.

2.2 Equilibrium Figure 2 shows the free body diagram for the vice-grip. Equilibrium conditions exist when the forces in the X and Y directions and moments in the Z direction are in equilibrium. This is achieved when the forces at A and B of Output 2 are set to be equal and opposite of one another. The link between C and D is always in equilibrium since it is a two-force member. The

last remaining equilibrium conditions are; moment equilibrium in the Z direction for Input 4 and Input 3, and force equilibrium in the X and Y directions for Input 3. The force, F, may be solved for using the following equations when T2 is known. Equilibrium of Input 3: ∑

(

)

( )

(2)

where Fx is the force in the X direction, F4 is the force through link 4, and

is the force through

joint B in the X direction. ∑

(

where Fy is the force in the Y direction and ∑

)

( )

(3)

is the force through joint B in the X direction.

(

)

(4)

where MC is the moment about joint C and r3 is the length of Input 3.

Equilibrium of Output 2: ∑

( )

(

)

(5)

where MA is the moment about joint A and r2 is the length of Output 2. ∑

( )

( )

(6)

Utilizing substitution, equations 2, 3, 4, and 6 give: ( )(

( ) ( )

( )

(

)

)

(7)

Equation 7 shows that as μ approaches 0 or π then the force, F, is 0. No reactive torque is able to overcome the force exerted. The vise-grip is able to clamp down on objects because it is a rocker-rocker. The mechanism approaches a dead position when links 3 and 4 are in line. At this

limit position, link 2 becomes the input in a geometric inversion of the four-bar. The vise-grip is able to â€œclampâ€? onto objects without losing its grip because of this dead position.

Figure 2: Equilibrium Forces and Moments on Vise-Grip