require mathematics and explanation
4.2 Question 2: Computational kinematics for three body system (8 marks)
Consider the three body multi-body dynamics system shown in Figure 2. which represents a cam system where the third body is ground. There arc two moving parts: cam and a lever. The cam (Part 1) is connected to ground by a revolute joint at the origin O. The lever (Part 2) can rotate around point 2P. while it slides against the cam at instantaneous point 2Q. Assume that there is a torsion spring at point 2P holding the lever against the cam. At this instant the cam is rotating with an angular velocity of 1£i . with an initial angular position of l0c. For this analysis we arc interested in the movement of the lever in this system. Your calculations may include determining the position, velocity and acceleration of points 2P and 2Q over a 180 degree rotation of Part 1.
Figure 2: Schematic of a three-body cam system.
Please state what the joints are in the system.
Then, using your knowledge of computational kinematics, determine the following:
• q
• C(q.r)
• !.c|
Since wc have not provided any values for the parameters in the system (c.g. lengths, positions, etc.), your equations should use the labels for the parameters according to the notation described in class.
You arc not required to solve this system. The question above, is simply asking you to set up the mathematics for the problem.
If you cannot do the mathematics, then please explain what you believe is the procedure to calculate each variable. Also, explain what each of the above variables mean. (This will allow you to obtain part marks for this question.)