We divided our kinematic analysis into two parts, the gripper movement and the movement of the entire arm. The gripper mechanism consists of two parallel 4 bar mechanisms that are driven together by two spur gears. The arm uses the same 4-bar mechanism but on a larger scale. We used the method we learned in class to analyze 4-bar mechanisms:
Using the calculations in Matlab, we plotted the kinematic position, velocity, acceleration, and overall motion of the mechanism.
Gripper Plots:
Figure 1: Theta 2 vs Theta 3
This plot describes the angle of link 3 in relation to link 2 which is the gear link of the gripper.
Figure 2: Theta 2 vs Theta 4
This plot describes the angle of link 4 in relation to link 2.
Figure 3: Theta 2 vs Omega 3
This plot describes the angular velocity of link 3 in relation to the position of link 2.
Figure 4: Theta 2 vs Omega 4
This plot describes the angular velocity of link 4 in relation to the position of link 2.
Figure 5: Theta 2 vs Omega 3
This plot describes the angular acceleration of link 3 in relation to the position of link 2.
Figure 6: Theta 2 vs Omega 4
This plot describes the angular acceleration of link 4 in relation to the position of link 2.
The overall motion of the gripper is uniform. Angle 4 and Angle 2 will always equal each other because it is a parallel system. Angle 3 will always be 0 relative to angle 2. This also allows for a consistent angular velocity and acceleration throughout the motion.
Arm Plots:
Figure 1: Theta 2 vs Theta 3
This plot describes the angle of link 3 in relation to link 2 which is the servo-driven link.
Figure 2: Theta 2 vs Theta 4
This plot describes the angle of link 4 in relation to link 2. Due to it being parallel the angles are the same as the arm moves.
Figure 3: Theta 2 vs Omega 3
This plot describes the angular velocity of link 3 in relation to the position of link 2.
Figure 4: Theta 2 vs Omega 4
This plot describes the angular velocity of link 4 in relation to the position of link 2.
Figure 5: Theta 2 vs Omega 3
This plot describes the angular acceleration of link 3 in relation to the position of link 2.
Figure 6: Theta 2 vs Omega 4
This plot describes the angular acceleration of link 4 in relation to the position of link 2.
Motion Plots:
Figure 1: Motion of Gripper
Figure 2: Motion of Arm