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

2. Segmental Angles

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

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

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

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

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

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

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

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

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

12. 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. Relative Motion: Joint Angles R thigh R shank

18. Joint Angles R thigh R shank R joint *R thigh = R shank R joint = R shank* R thigh ’ R joint General form: R joint = R distal* R proximal ’

19. Joint Angles flexion abduction Internal/external R joint = R distal* R proximal ’

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

21. Joint Angles: Gimbal Lock flexion ab/adduction Internal/external What happens if the ab/aduction angle approaches 90 degrees? R joint = R distal* R proximal ’

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

23. Helical Angles* *From: Kinzel, Hall and Hillberry, J Biomech, 5, 1972 “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”. Y X Z

24. Helical Angles* *From: Kinzel, Hall and Hillberry, J Biomech, 5, 1972 “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 ”. Y X Z 

25. Helical Angles* *From: Kinzel, Hall and Hillberry, J Biomech, 5, 1972 “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 ”. Y X Z  Rotation:

26. Exporting Data from GaitProject to Visual3d

27. Assignment #7 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