A generalized method for determining load workspace of spatial parallel mechanisms

An analytical-numerical method based on solution of inverse dynamics is presented for determining the load workspace of generally configured parallel motion systems with up to 6 degrees of freedom. The kinematic workspace is also obtained by the method, since the solution of inverse kinematics is embedded in the procedure. The method is first developed for 3DoF motion systems to take the advantages of illustrating the workspace by use of 3D plots. Then it is extended to higher degrees of freedom. For such types of 3DoF motion systems, a generalized trajectory is defined for the manipulator in the kinematic workspace that consists of straight paths connecting 26 selected points of workspace's boundary. The platform performs piecewise sinusoidal movements on the trajectory such that it stops at each of the selected point and goes ahead toward the other with maximum allowable speed. As the platform moves on this trajectory, legs are exposed to any possible static and dynamic forces. The forces obtained in this way are used to determine the force workspace which is defined as the subspace of kinematic workspace in which the structural forces do not exceed their critical values. In this paper, the criterion of structural failure is considered to be the buckling of legs. The generalization of the method to higher degrees of freedom is straightforward. As case studies, a 3DoF heave-roll-pitch motion platform and a hexapod are chosen to apply the method to. The results of the method can be used in the design of both the control system and structure of parallel manipulators. The method is also advantageous in structural design of large sizes motion systems in flight simulator application.