Analysis Of Parallel Mechanism Research Articles

Kinetostatic Analysis of 4-R(CRR) Parallel Manipulator with Overconstraints via Reciprocal-Screw Theory

The paper proposes a new approach based on reciprocal screw theory to analyze kinetostatics of lower-mobility parallel mechanisms with overconstraints and static indeterminacy. For force analysis of parallel mechanisms, the main reactions should be solved firstly, and then all other constraint reactions are easy to be obtained. The approach can remarkably reduce the number of unknowns and keep the number of simultaneous equilibrium equations not more than six each time. For static indeterminacy, it also needs to set some complementary equations. All active forces and constraint reactions of the kinematic pairs can be simultaneously obtained by analyzing the equilibrium of everybody one by one. A 4-R(CRR) parallel manipulator with collinear-force static indeterminacy is taken to introduce the method, which indicates that the method is simple and effective.

Mobility Bifurcation of Two 1R3T Parallel Mechanisms Based on Lie Group

Mobility bifurcation of 1R3T (R—rotational,T—translational) parallel mechanisms is studied by applying Lie group theory. Some theoretical fundamentals necessary for application of Lie group theory to mobility analysis of parallel mechanisms are briefly reviewed. Mobility analysis of the 2-xPyRyRxRxR/yPxRxRyRyR and 2-xPyRuPxRxR/yPxRvPyRyR parallel mechanisms is performed. It is proved that the two parallel mechanisms have mobility bifurcation with displacement set of the moving platform being {X(x)}∪ {X(y)}. Further,it is obtained that the limb displacement manifold of the 1R3T parallel mechanism with mobility bifurcation is {G(x)}{G(y)} or {X(x)}{R(N,y)}. The structural geometrical conditions of the 1R3T parallel mechanism with mobility bifurcation are also presented. When the moving platform is parallel to the base,the parallel mechanism is in a singular configuration and the moving platform has five instantaneous degrees of freedom. The mobility bifurcation happening in this singular configuration requires five actuators to control the motion of the moving platform.

Kinematic analysis of parallel mechanisms at singular points where a connecting chain has local mobility

In the present paper, singular point of parallel mechanisms where a connecting chain has local mobility has been investigated. Through inverse kinematics of each connecting chain, the presence of such a singular point has been revealed. The kinematic relationship between the output velocity and the velocities of both active and passive joints in the connecting chain with local mobility has been derived. Utilizing this relationship, a method generating a trajectory to pass through such a singular point has been proposed. Numerical examples of a planar parallel mechanism with three degrees of freedom have been shown and discussed.