Theory & Design

Methods

To develop 1-DOF underactuated gait rehabilitation robot, we employed the Theo Jansen mechanism for the ankle path generation. Then we formulated the optimization problem, which minimizes the difference between healthy subject's ankle trajectory and the kinematic end point of Theo Jansen mechanism as follows:

where L₁-L₁₂ are the link lengths, p_human(t_k) is the ankle position of human gait motion capture data at time frame k, p_jansen(t_k,L) is the kinematic end point of Theo Jansen mechanism at time frame k, Φ is the rotation angle of the ground and τ is the phase lag. For the human gait motion, the trajectories of one individual subject is applied.

The optimization results are shown below. The size of the trajectory is scaled down to the size of the prototype (about 1/9.5 of the actual human ankle trajectory).

 Knee Joint Trajectory

After finding the ankle position with the optimization, the knee joint trajectory is found by simply using 2 planar robot mechanism. Once the lengths of thigh and shank are given, the trajectory of knee joint can be calculated by solving the inverse kinematics of the following equation given by

where p_ankle,x and p_ankle,x are the ankle trajectories of x-axis and y-axis, respectively,  l₁ is the thigh length,  l₂ is the shank length, θ₁ andθ₂ are the hip and knee joint angles, respectively (see figure below). The result of the knee joint trajectory is shown below.