How can I calculate kinematics of ankle joint after calculating local coordinates of the foot and shank from the 3D position of markers?

Hi all,

I have a human 3D motion data (walking straight).

I want to calculate ankle joint kinematics.

I have calculated the local coordinates of the foot and shank segments using the XYZ coordinates (in meters) of 3 markers from each segment. Code for shank coordinate system ( as suggested by ChatGPT):

% The shank coordinate system axes (lateral malleoli, medial malleoli, head of fibula)
l_shank_x = (llmal - lmmal) / norm(llmal - lmmal);
l_shank_y = cross(l_shank_z, l_shank_x);
l_shank_z = cross(lfib - lmmal, llmal - lmmal) / norm(cross(lfib - lmmal, llmal - lmmal));
% Ensure axis vectors are normalized
l_shank_x2 = l_shank_x / norm(l_shank_x);
l_shank_y2 = l_shank_y / norm(l_shank_y);
l_shank_z2 = l_shank_z / norm(l_shank_z);
% Create the shank rotation matrix
lshank_rotation_matrix = [l_shank_x2', l_shank_y2', l_shank_z2'];

These coordinates are attached for both the foot and the shank (both 868x9 double).

I have also calcuted ankle joint center (attached):

  l_ankle_cent = lcal + lmet5/2;

I wonder what is the general framework to follow to calculate ankle joint 3D kinematics (in degrees) from here?

Answer 1

[Suraj Kumar]

Hi Tomaszzz,

To compute the ankle joint angles, you can refer the following steps and the attached code snippets:

1. Compute the relative rotation matrix between the shank and the foot by multiplying the inverse of shank’s rotation matrix and foot rotation matrix.

for i = 1:num_frames 
   % Extract rotation matrices for the current frame 
   shank_rot = lshank_rotation_matrix(:, :, i); 
   foot_rot = lfoot_rotation_matrix(:, :, i); 
   % Calculate relative rotation matrix 
   relative_rotation_matrix = shank_rot' * foot_rot;

2. Then, you can extract the Euler angles using the ‘rotm2eul’ function and iterate over each frame, performing the above calculations for all frames in the dataset.

% Convert to Euler angles using ZYX sequence  
euler_angles = rotm2eul(relative_rotation_matrix, 'ZYX'); 

3. Plot the calculated ankle joint angles over time to visualize the results.

figure; 
subplot(3, 1, 1); 
plot(ankle_angles_degrees(:, 1)); 
title('Ankle Joint Yaw Angle'); 
xlabel('Frame'); 
ylabel('Degrees'); 

subplot(3, 1, 2); 
plot(ankle_angles_degrees(:, 2)); 
title('Ankle Joint Pitch Angle'); 
xlabel('Frame'); 
ylabel('Degrees'); 

subplot(3, 1, 3); 
plot(ankle_angles_degrees(:, 3)); 
title('Ankle Joint Roll Angle'); 
xlabel('Frame'); 
ylabel('Degrees'); 

You may check the output below for a better understanding:

To know more about the ‘rotm2eul’ function in MATLAB, you can refer to the following documentation:

• https://www.mathworks.com/help/robotics/ref/rotm2eul.html

Happy Coding!