Analysis of simplified position and 5-DOF total orientation workspaces of a hexapod mechanism

The exact positional and total orientation workspaces of a hexapod parallel mechanism are three-dimensional volumes that are too complicated for an operator to make use of, but a knowledge of them is indispensable in order to avoid collisions with the environment and to locate the workpiece. Fortunately, the positional and total orientation workspaces of a symmetric simplified architecture (the SSM type) can be bounded from inside and outside by ellipsoids symmetric about the z-axis. Accordingly, this paper presents closed-form solutions for the radii of the inscribed and circumscribed circles of the positional workspace and approximate solutions for the total orientation workspace at any given height. These solutions can be plotted on a two-dimensional graph that is convenient for an operator on the shop floor. Furthermore, these solutions can be developed into a simple procedure for the design of a prescribed workspace.