Five-bar linkage

In kinematics, a five-bar linkage is a mechanism with two degrees of freedom that is constructed from five links that are connected together in a closed chain.

As the motor can be quite massive, this significantly decreases the total moment of inertia of the linkage and improves backdrivability for haptic feedback applications.

Both the forward and inverse kinematics of this robotic configuration can be found in closed-form equations through geometric relationships.

[2] Dynamic modeling of this robotic configuration has been done by Khalil and Abu Seif,[5] forming an equations of motion relating the torques applied at motor with the angles at the joints.

[7] A prosthetic ankle-foot by Dong et al. used a geared five-bar spring mechanism to simulate the stiffness and damping behavior of a real foot.

Animation of a five-bar mechanism angle sweep over its workspace, done on MATLAB . The red arrow indicates the velocity direction of the end-effector due to unit speed input at the left motor and its length is proportional to its speed.
Velocity ellipses of a five-bar linkage robot.