Kinematics and dynamics of Jansen leg mechanism: A bond graph approach

The Jansen mechanism is a one degree-of-freedom, planar, 12-link, leg mechanism that can be used in mobile robotic applications and in gait analysis. This paper presents the kinematics and dynamics of the Jansen leg mechanism. The forward kinematics, accomplished using circle intersection method, determines the trajectories of various points on the mechanism in the chassis (stationary link) reference frame. From the foot point trajectory, the step length is shown to vary linearly while step height varies non-linearly with change in crank radius. A dynamic model for the Jansen leg mechanism is proposed using bond graph approach with modulated multiport transformers. For given ground reaction force pattern and crank angular speed, this model helps determine the motor torque profile as well as the link and joint stresses. The model can therefore be used to rate the actuator torque and in design of the hardware and controller for such a system. The kinematics of the mechanism can also be obtained from this dynamic model. The proposed model is thus a useful tool for analysis and design of systems based on the Jansen leg mechanism.