Problem 1: The vector coordinates of two points P and P' on a rigid body are given in five different positions in the table below.
1) Determine the finite center of rotation and the increment in the angle of rotation from position 2 to position 3.
2) If time interval t = 0.1 sec, determine the velocity and acceleration of the point P at position #3. (Unit of coordinate: mm)
Position Px Py P'x P'y
1 0.00 0.00 1.00 0.00
2 0.873 0.411 1.76 0.881
3 1.16 1.01 1.86 1.73
4 0.94 2.00 1.24 2.96
5 0.328 2.47 0.312 3.48
Problem 2: The coordinates of three points of a rigid body, in their initial positions P1, P2, and final positions P1', P2', P3' are given below.
x y z
P1 1.000 0.000 0.000
P2 4.000 0.000 0.000
P3 1.000 2.000 0.000
P4 2.488 -1.065 0.9107
P5 5.220 -0.333 1.911
P6 1.821 0.7564 1.399
1) Find the rotation matrix R and translation vector T describing the rigid body motion from the initial position to the final position.
2) From R, determine the rotation angle and the unit vector of the helical axis.
