8.8 Problems

1. Draw the kinematic inversions of the linkage below. Does it satisfy the Grashof Criterion? What is the mobility of the mechanism? Determine the maximum transmission angles, and the toggle angles if CD is the crank. What is the advance-to-return time ratio?

2. Draw the kinematic inversions of the linkage below. Does it satisfy the Grashof Criterion? What is the mobility of the mechanism?

3. The human arm is an open loop kinematic chain. Assuming the shoulder is the ground, what is the mobility of the human arm, including all joints down to the finger tips?

1. We have been asked to design a coarse pitch (P=3) gear pair with stub teeth and a speed ratio of e=0.24. Find the radii and dimensions needed to draw the gears. Find at least one point on a gear tooth profile. Roughly sketch the gears showing the dimensions calculated.

1. You were recently hired as a Fuel Containment and Monitoring specialist for Generous Motors. Your first job is to design a mechanical gauge for an instrument panel. The tank holds up to 10 gallons of fuel. It has been determined that the needle on the gauge should remain steady at the full ‘F’ mark while the tank contains 8 to 10 gallons. When the tank has less than 3 gallons the gauge should read empty ‘E’. The last design was a failure ‘F’, and your boss fired the engineer responsible. It seems that he his design did not follow good cam design rules - the velocity and accelerations were not minimized - and so the gauge would wear out, and jam prematurely. Design a new cam to relate the float in the tank to the gauge on the instrument panel.

2. The motion profile curve below has 4 segments. Segments A and C are based on polynomials. Segment D is based on a harmonic/cosine function. Segment B is a constant velocity segment.

a) Write the equation for curve segment B.

b) What effect does the follower shape have when converting the motion profile to a cam profile. Draw a figure to illustrate this with a round follower.

c) Write the coefficients for the curve segment C.