E. RRG Gripper Analysis

Figure 11. Link 3 Position vs. Input Angle

To do the analysis on the mechanism we used the vector loop method. All of the graphs are for the mechanism moving from the closed position to extended position only. The slider position was used to find what arm size would give us base dimensions that could most closely resemble that of the Robotiq gripper. The distance that the slider travels is equivalent to the length of the base. We chose this length because this minimized the total volume but also allowed us to fit the electronics within the base.

Figure 13. Path of Gripper Bolts

The graph above represents the path traveled by the actual gripper part of the mechanism. We used the location of the bolts to determine the actual position of the gripper, which is between the bolts. The position on the base was chosen such that we could get the straightest path in the extending motion for most accurate gripping/pinching of objects. We also found an appropriate length driver arm that can reach outwards to grip cans similar to what the existing robot does. The length needed to be long enough to extend but also not too long or there would be too much torque on the joints between links and cause instability. 

Figure 15. Link 3 Angular Velocity vs. Input Angle

Figure 16. Link 3 Angular Acceleration vs. Input Angle

The angular acceleration of the link 3 matches the velocity profile. 

Figure 12. Slider Position vs. Input Angle

We used the position of the intermediate link that rotates between the driver arm and the slider to determine the slider position and velocity. 

Figure 14. Slider Velocity vs. Input Angle

Slider velocity graph was used mainly to validate the equations being used for analysis. The velocity of the slider is proportional to the speed at which the motor is driven. 

The mechanical advantage of our mechanism is m_A= 0.84. This was calculated using the equation m_A=(w_in* r_in)/(w_out*r_out). The motor connects to a gear that is identical to all the other gears in our mechanism this makes our velocity ratio 1 and makes it easier for us to control the gripping motion.  

Unfortunately, we were not able to fit a better gear train to increase the mechanical advantage without creating acrylic gears that would snap under the torque. In the future, the gears would be made from metal. A big constraint in this project was the amount of space available for the gear train as well as the electronics. In our final design, we are two inches larger in total base width than the Robotiq, but were able to reduce the length of the fingers just over 3 inches.