Jacobian Based Kinematic and Static Analysis of Over-Constrained Mechanisms with Prismatic and Revolute Joints

摘要

Over-constrained and deployable mechanisms are extensively used in space and in other applications. There is an existing approach which studies the mobility and static analysis of the over-constrained and deployable mechanisms. The main feature of this approach is that the natural co-ordinates are used to define all the constraints present in the mechanisms. The constraint Jacobian matrix is developed by taking the derivatives of all the constraint equations. The null space dimension of the constraint Jacobian matrix gives the degree of freedom of the over-constrained mechanism. A numerical algorithm is used to identify the number of redundant links and joints through the constraint equations. Closed-loop kinematic solutions are found out to ensure that the over-constrained mechanism can be made deployable by actuating only one joint and all other points can be expressed in terms of this actuated variable. In this paper, the existing approach has been extended by implementing the same in an over-constrained box mechanism, where the trajectory of the joints obtained by using the constraint equations has been compared with the trajectory obtained from ADAMS. We have also extended the same approach to static analysis for an over-constrained hexagonal mechanism. The result obtained has been cross checked with that of obtained in ANSYS. Above all the new contributions of this paper is that we have used the approach for studying kinematics and statics of a mechanism having both prismatic and revolute joints which has not been done before. Secondly, the validation of the proposed theory has been done by using the above mentioned commercial packages.