Homework #4 Due 2/13/08

Read: Craig, Ch.2

1. 

(a)Develop the 4x4 homogeneous transformation matrix T(q₁,q₂) that relates [^oP_X ^oP_Y ^oP_Z]^T to [²P_X ²P_Y ²P_Z]^T

according to

[^oP_X ^oP_Y ^oP_Z 1]^T =[T(q₁,q₂)][²P_X ²P_Y ²P_Z 1]^T

for any point P, for our system above.

(b) Recover the kinematics expressions for P, from the first homework, by applying

this transformation to [²P_X ²P_Y ²P_Z]^T=[L₂ 0 0]^T

2. Use the homogeneous transformation matrix derived in class to

express the position of the red point, located a distance L₃ as indicated from joint 3 relative to

the stationary O frame, as a function of q₁, q₂, q₃.

3. Craig, problem 2.37