Kinematics Analysis and Synthesis of Mechanisms

(MEC 567- Spring 2015) Final Exam

1. Why do we use complex numbers to derive position, velocity and acceleration

equations in planar linkage mechanisms? What are the limitations of complex numbers? (5 points)

2. Using a graphical method, design a four-bar linkage (hinge) mechanism for opening and closing a kitchen cabinet door shown in Figure 1. Make all the appropriate assumptions for designing such a cabinet door hinge. Clearly show each and every step that you have followed together with the reason and why it works. (25 points)

3. Using complex numbers, find the motion (angular position and velocity) of the links of the mechanism of problem (2) if the cabinet door is opened at a constant velocity. (15 points)

4. Consider a spatial 2PR robot manipulator that is to be used to position objects in the desired position in the workspace of the manipulator.

Draw the robot manipulator and clearly indicate its Denavit and

Hartenberg coordinate systems and notations. (5 points) Pick a set of link parameters that would simplify its inverse dynamics

calculations. (5 points) Derive the homogeneous transformation matrices that can be used to

derive the direct kinematics relationships. (5 points) Derive the direct kinematics relationships using:

The transformation matrices. (5 points) Direct geometrical relationships. (5 points)

Write the direct kinematics equations for this robot manipulator in terms of the position of the payload and then derive the displacement transmissibility relationships for this manipulator and explain its meaning in terms of displacement, velocity and force transmission. (15 points)

Derive the equations of motion for this robot manipulator. (15 points)

5. Draw up the feed-forward based control look for the above robot manipulator.

What are the advantages and disadvantages of using feed-forward control. (10 points)

Figure 1