Velocity similarity principle V(θ., ṡ, ub, Qb) = DabV (θ., ṡ, ua, Qa)D ab–1 is presented and used to derive several useful forms of the Jacobian matrix for the manipulator from its basic kinematic equations in 4 X 4 matrix form. The zero reference position representation is used and, therefore, the base system is the only coordinate system utilized in the derivations. For manipulators with a spherical wrist, a modified form of the Jacobian is presented in which the Jacobian columns corresponding to the regional structure are completely decoupled from those corresponding to the wrist structure.

In this paper, a very inexpensive, lightweight and simple wrist mechanism is introduced. This wrist displays nonlinear torsional vibrations. This differs from conventional wrists in that structural flexibility in the mechanism is allowed to occur by design. In this paper, the dynamic equations of this wrist are derived. System identification techniques are then employed to obtain a linearized model. Various control strategies are studied. It is shown that the input-output feedback linearization technique is not feasible for these nonlinear dynamic equations. It is also shown that the use of conventional rigid body PID controllers on this proto-type is inadequate. A tracking controller which compensates for the flexible dynamics of the wrist is implemented with encouraging results. This controller allows the end-effector to be placed at an arbitrary orientation with little vibration. The effect of the controller is to make the wrist appear to have a much higher structural stiffness. The compliant nature of this wrist allows simple force control strategies to be implemented. It is the combination of the wrist with the control algorithm which makes this design viable.

A new kinematic design of a parallel spherical wrist with actuatorredundancy is presented. A special feature of this parallel manipulator is thearrangement of co-axial actuators which allows unlimited rotation about any axisinside a cone-shaped workspace. A detailed kinematic analysis has shown thatactuator redundancy not only removes singularities but also increases workspacewhile improving dexterity. The structure optimization has been performed with aglobal dexterity criterion. Using a conditioning measure, a comparison with anon-redundant structure of the same type was performed and shows that asignificant improvement in dexterity has been obtained.