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188.8.131.52 Reaction Moments from Torsional Springs
The reaction moment generated by a torsional spring acting on rigid body is given by where is the angular gap function between the bases of rigid bodies and , is the (optional) Lagrange multiplier used when invoking the augmented Lagrangian method, and is a penalty parameter representing the torsional spring stiffness. We consider three cases for the choice of : For example, is used to model the reaction moment in a prismatic joint, whereas is used with revolute, cylindrical and planar joints.
Now, the linearization produces where and Therefore, in the expression for in (7.9.1-7), we have