Force distribution in closed kinematic chains

The problem of force distribution in systems involving multiple frictional contacts between actively coordinated mechanisms and passive objects is examined. The special case in which the contact interaction can be modeled by three components of forces (zero moments) is particularly interesting. The Moore-Penrose generalized inverse solution for such a model (point contact) is shown to yield a solution vector such that the difference between the forces at any two contact points projected along the line joining the two points vanishes. Such a system of contact forces is described by a helicoidal vector field which is geometrically similar to the velocity field in a rigid body twisting about an instantaneous screw axis. A method to determine this force system is presented. The possibility of superposing another force field which constitutes the null system is also investigated