calculating position using follower wheels

[Ether]

Originally Posted by Ether

A certain robot with a 3 degree-of-freedom drivetrain (FWD, STR, RCW) is on a flat level floor. At time T=0, its center of geometry (CoG) is located at the origin of an XY coordinate system fixed with respect to the floor; it is facing 15 degrees clockwise from the +Y axis; and it has the the following robot-centric constant motions:

forward = 5 ft/s
strafe_right = 4 ft/sec
rotate_CW = 120 degrees/sec

Question 1: What are the coordinates 3 seconds later, and what direction is the robot facing?

Question 5: Same as Question 1 (above), except:

forward = 5*sin(t/2) ft/s
strafe_right = 4*sin(t/2.2) ft/sec
rotate_CW = 1.5*sin(t/2.5) radians/sec

5a) What are the XY coordinates 30 seconds later?

5b) What is the path length traveled during that 30 seconds?