Biomedical Engineering Biomechanics Homework

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.

 

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