3) Kinematic Analysis and Synthesis Group 13

Mobility Calculation: In each arm there are four links, four full joints, and zero half joints. This results in one degree of freedom.

L = 4, J1 = 4, J2 = 0

M = 3(L - 1) - 2J1 - J2 = 3(4 - 1) - 2(4) - 0 = 1 DOF

The tip of the hook had a range of motion of 2.11 inches along the x-axis and 2.37 inches along the y-axis. The total step size from when the hook contacted the ladder to when it stopped contacting is 1.66 inches. The desired motion was a half ellipse where the flat portion would occur when the hook was in contact with the ladder, to maximize the forward motion. The step motion occurred between 28 and 163 degrees.

Figure 3.1: Plot of X and Y position of the tip of the hook of the fourbar mechanism.

Figure 3.2: Plot of the velocity of the tip of the hook of the fourbar with respect to the input angle.

We designed the motion of the fourbar mechanism to trace a largely straight path for part of the motion so that we can have a smooth climbing motion up the ladder. The rounded part of the path is so that we can extricate the end effector from the ladder and move it back into position to interact with the next rung. 

Figure 3.3: A GIF of the path that the fourbar mechanism was to follow for our robot.

Figure 3.4: Part 1 of Position Analysis of the fourbar mechanism

Figure 3.5: Part 2 of Position Analysis of the fourbar mechanism

Figure 3.6: Part 3 of Position Analysis of the fourbar mechanism

Figure 3.7: Velocity Analysis of the fourbar mechanism