Linkage Design and Mechanical Advantage

Linkage Synthesis:

The main goal of our mechanism was to use the power of the motor to apply a large force, just as normal pliers magnify the user's grip strength. To accomplish this, we designed the mechanism to maximize mechanical advantage. Since static forces were our only interest, velocity and acceleration analysis were not carried out. 

Due to the symmetry of our mechanism, the position analysis could be completed by treating each half our mechanism (divided along the axis of the lead screw) as a slider-crank. The input to the mechanism was the lead screw nut ("the slider") and the output was the plier head ("the crank"). This allowed us to develop an extremely simple formula to determine the MA at each position:

Where:

a = the distance from the plier pivot to the attachment to link b

r= the length of the plier head

The angles ϴ­₂ and ϴ₃ were calculated using the position analysis for an offset slider-crank. We then developed a matlab code implementing these functions and graphing the linkage mechanical advantage for the range of motion of the mechanism. Using this code, we modified the link lengths to determine the optimal mechanical advantage based on the design constraints of our mechanism. Below is an outline of our process.

1. Link C: we found that minimizing the offset gave us a greater mechanical advantage. Thus, length C was minimized while still allowing clearances for the links to rotate. 
2. Length R: the length of the plier head was chosen to mirror those of traditional needle nose pliers. 
3. Length A: Increasing link length A increased our mechanical advantage. However, it also increased the overall size of our mechanism. Since the device was designed to be strapped to Paul's arm, we did not want it to be too cumbersome. For this reason we chose to keep the total width of the device less than 14 cm, which allowed us to determine length A through simple geometry.
4. Length B: To maximize mechanical advantage, we designed link B so that it would be perpendicular to the axis of the lead screw when the pliers were fully closed. 

The resulting plot of mechanical advantage can be seen to the right. Notice that the mechanical advantage is highest when the pliers are fully closed and lowest when fully open. 

Also, this is only the mechanical advantage of the linkage itself. The lead screw further adds mechanical advantage to the system:

This allowed us to achieve an extremely high mechanical advantage for our device.