Consider a mechanical bull mechanism as shown in Figure 1(a). The saddle is mounted to the link 3 using an attachment as shown in Figure 1(b) which is rigidly welded to link 3 as shown.

Task 1: Consider a rider who weighs 80 Kg. Perform a dynamic force analysis on the mechanism and find the contact force between the rider and the saddle assuming the rider cannot slide along the saddle. Find the motor speed at which the rider loses contact with the saddle. Based on the torque requirements, spec out a motor that you can use for this mechanism. You can represent the rider as a point mass located at point GR.

Task 2: Consider the same rider of mass 80 Kg riding this bull. The input is rotating at 5 rad/sec. At this speed, consider the forces between the rider and the saddle and perform a static failure analysis using von Mises yield criterion for the saddle post beam of diameter d. Find the factor of safety for all positions of the input for the given dimensions of the saddle. Further, size the beam to guard against failure with a factor of safety of 2(minimum). Assume the saddle itself is sturdy enough to not fail. The beam is made of steel for which material properties are specified in Table 1.

Task 3: Based on the forces derived in task 1, conceptually determine which link is most likely candidate for fatigue failure. Support your claims with results from force analysis.

Deliverables: The following deliverables are to be turned in to your TA.

1.) Accelerations of the mass centers of the links and the rider at the input positions θ2= 60°, 180° and 330°. Due: Second lab session, the week of October 19th.

2.) Internal reaction forces for the four bar mechanism and the motor torque at the input positions θ2= 60°, 180° and 330°. Due: second lab session in the week of October 26th.

For the final report discuss, among other things but not limited to: Comments on the general working of the mechanism. What is the nature of forces between the rider and the saddle, and how does speed of input influence these. Is there a speed for which the rider will not be in contact with the saddle at all? Discuss the effect of changing the input velocity on the internal reaction forces of the mechanism and the required torque. Discuss the impact of velocity on the state of stress during static failure analysis for a fixed position of input. Is there a practical significance behind considering the COM of the rider offset from point E? What differences do you expect to observe if the COM coincides with point E?

Following table summarizes the constants of the system:

Table 1: Material Properties, Masses and Link Lengths