Tonights Lecture Segmental Angles Joint Angles Euler Joint

Tonight’s Lecture • • Segmental Angles Joint Angles: Euler Joint Angles: Helical Exporting Data from Gait. Project to Visual 3 d

Segmental Angles

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

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

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

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

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

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

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

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

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

Rotation Matrices 3 D

Rotation Matrices 3 D

Euler Angles: Simple Method

Euler Angles: Robust Method (handles angles from -180 to +180) Atan 2(x, y) is the arc tangent of x/y in the interval [-pi, +pi] radians

Joint Angles

Relative Motion: Joint Angles Rthigh Rshank

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

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

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

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

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

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

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

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

Exporting Data from Gait. Project to Visual 3 d

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 Visual 3 d • Run Visual 3 d IK • Create Reports Comparing the joint angles obtained by all three methods