A new approach to orientation workspace analysis of 6-DOF parallel manipulators

A Complete Method for Workspace Boundary Determination on General Structure Manipulators

“…Its full workspace is 6-D, and its boundary 5-D, which hinders any attempt of computing it exhaustively, due to the curse of dimensionality. For this reason, and because 6-D spaces are impossible to visualize directly in three dimensions, comprehension on this workspace is being gained by obtaining lower dimensional workspaces like 1) the constant orientation workspace, or set of attainable locations by a point P on the platform, for a fixed platform orientation [18], [42], 2) the constant position workspace, or set of platform orientations for a fixed position of P [22], [43], [44], [45], and 3) the reachable workspace, or set of locations that P can attain, with at least one platform orientation [46], [47]. All of these workspaces can be computed by the proposed technique using a proper choice of the u variables and fixing others to given values.…”

“…Because of the complexity of their defining equations, orientation workspaces are considered among the most difficult ones to compute and represent [7], [22], [44], [45]. Their derivation could be illustrated on the Stewart platform, but we shall do so on spherical parallel manipulators (SPM) because this will lead to one example of the degenerate barriers mentioned in Section III, which the method in [31] is unable to identify.…”

“…Other significant approaches include interval analysis or discretization techniques for Gough-type manipulators [21], [22], optimization-based algorithms for fully serial or parallel robots [4], analytic methods for symmetrical spherical mechanisms [23], and analytic, topologic, or algebraic-geometric procedures for serial manipulators [24]- [28].…”

“…Even discretization methods, which resort to configuration sampling only [17], [22], [30], rely on the assumption that either the forward or the inverse kinematics problems have a simple solution, which need not be the case in general.…”

Determining workspace parameters for a new type of 6RSS parallel manipulator based on structural and geometric models

“…Regardless of the number of degrees of freedom, fewer [1][2][3][4][5][6][7][8] or more [9][10][11][12], the parallel mechanisms have proven their utility in various domains such as flight simulators, telescope position control, radar antennas, pointing devices [13].Parallel mechanisms have a robust construction and can move bodies of considerable mass and size at high speed, establishing a translational motion or rotation of the mobile platform. Compared to serial mechanisms, parallel manipulators have some special characteristics: high rigidity, high dynamic loading capacity, chain closed structure, high positional accuracy.…”