Fundamentals of Biomechanics

BME375 Fundamentals of Biomechanics
Homework III
Problem 1:
The vector coordinates of two points P1 and P2 on a rigid body are given in five different poisons
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 P1 at position

3. (Unit of coordinate: mm)

Position P1x P1y P2x P2y
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, P3) and final
position (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
P1’ 2.488 -1.065 0.9107
P2’ 5.220 -0.333 1.911
P3’ 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 and T, determine the rotation angle and the unit vector of the helical axis.