SummaryAn approach for calculating the maximum possible absolute values of joint velocities or generalized reactions in a leg of a parallel mechanism has been considered in this paper. The Jacobian analysis and the Screw theory-based methods have been used to acquire the result. These values are calculated for the “worst” directions of the external load or end-effector’s velocity for each leg. The feasibility of using these parameters as the measures of closeness to different types of parallel mechanism singularity is discussed. Further, how this approach is related to the state-of-the-art methods has been illustrated. The key aspect of the discussed approach is that the normalization of vectors or screws is carried out separately for angular and linear components. One possible advantage of such an approach is that it deals only with the kinematic and statics of the mechanism while still providing physically meaningful and practically applicable measures. Case studies of a 3-Degrees Of Freedom translational parallel mechanism and a planar parallel mechanism are presented for illustration and comparison.
This article presents the velocity and singularity analysis for a five-degree-of-freedom (5-DOF) parallel-serial manipulator. The hybrid structure of the manipulator combines a tripod-like parallel part and a serial part, represented as two carriages moving in perpendicular directions. This manipulator provides its end-effector with a 3T2R motion pattern, which includes three independent translations and two independent rotations. First, the study briefly discusses the manipulator design and the results of the position analysis. These results form the basis for the subsequent velocity and singularity analysis, performed by screw theory. The screw coordinates of the unit twists are written for each manipulator joint, and then through the reciprocal screw approach, the actuation and constraint wrenches of the manipulator are obtained by simple inspection. Based on these twists and wrenches, the paper forms the velocity equation and shows an example of the inverse velocity analysis for a given end-effector trajectory. The same example is solved by numerical differentiation to verify the proposed approach. Next, the paper investigates singular configurations by analyzing the wrench system of the manipulator and presents several conditions for serial and parallel singularities. Each condition has both a symbolic representation, given by an equation for screw coordinates of certain wrenches, and a visual representation, which shows the manipulator in a singular configuration.
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