Segmental Angles Joint Angles: Euler Joint Angles: Helical

1. Tonight’s Lecture Segmental Angles Joint Angles: Euler Joint Angles: Helical Exporting Data from GaitProject to Visual3d

2. Segmental Angles

3. Y Y’ X Rotation from Global to Local P X’ X Z Z’

4. Y Y’ X Rotation Local to Global P X’ X t Z Z’

5. Y Y’ Y Rotation from Global to Local P X’ X Z Z’

6. Y Y’ Y Rotation from Local to Global P X’ X Z Z’ t

7. Y Y’ Z Rotation from Global to Local X’ P qz X Z’ Z

8. Y Y’ Z Rotation from Local to Global X’ P qz X Z’ t Z

9. About the x axis About the y axis About the z axis Y Y X X Z Z Orientation of Bodies in 3D

10. About the x axis About the y axis About the y axis About the x axis The final orientation depends on the rotation sequence Y X Z

11. Rotation Matrices 3D • Rotation’s depend on the order they are applied

12. Rotation Matrices 3D

13. Rotation Matrices 3D

14. Euler Angles: Simple Method

15. Euler Angles: Robust Method (handles angles from -180 to +180) Atan2(x,y) is the arc tangent of x/y in the interval [-pi,+pi] radians

16. Joint Angles

17. Rthigh Relative Motion: Joint Angles Rshank

18. Rjoint*Rthigh = Rshank Rjoint Rjoint = Rshank*Rthigh’ Rthigh Joint Angles General form: Rshank Rjoint = Rdistal*Rproximal’

19. Rjoint = Rdistal*Rproximal’ Joint Angles abduction flexion Internal/external

20. Red – flexion extension (thigh) Green – ab/adduction (float) Blue – internal/external (shank) Lower Extremity: Joint Coordinate System

21. Rjoint = Rdistal*Rproximal’ ab/adduction flexion Joint Angles: Gimbal Lock Internal/external What happens if the ab/aduction angle approaches 90 degrees?

22. Solutions: • Use alternative Euler Sequence (for example ZYZ is the ISB • recommended sequence for the shoulder) • Helical Angles Joint Angles: Gimbal Lock

23. Y X Z “The displacement of a moving body from position 1 to position 2 can always be represented as a rotation about, and a translation along, a unique axis located Somewhere in the fixed body”. Helical Angles* *From: Kinzel, Hall and Hillberry, J Biomech, 5, 1972

24. Y X Z “The displacement of the moving body is completely defined if the location and inclination of the screw axis, the rotation angle , and the translation magnitude K are know ”. f Helical Angles* *From: Kinzel, Hall and Hillberry, J Biomech, 5, 1972

25. Y X Z “The displacement of the moving body is completely defined if the location and inclination of the screw axis, the rotation angle , and the translation magnitude K are know ”. f Rotation: Helical Angles* *From: Kinzel, Hall and Hillberry, J Biomech, 5, 1972

26. Exporting Data from GaitProject to Visual3d

27. Compute and Export the Joint Angles for the Ankle, Knee and Hip using the • Non-Optimal Method (3 files) • Compute and Export the Joint Angles for the Ankle, Knee and Hip using the • Optimal Method (3 files) • Import All Exported Joint Angles (6 files) into Visual3d • Run Visual3d IK • Create Reports Comparing the joint angles obtained by all three methods Assignment #7