A PRACTICAL QUALITY INDEX BASED ON THE OCTAHEDRAL MANIPULATOR

The octahedral manipulator is a ''3-3'' device that is fully in parall el. It has a linear actuator on each of its six legs. The legs connect an equilateral platform triangle to a similar base triangle in a zigz ag pattern between vertices. Our proposed quality index takes a maximu m value of 1 at a central symmetrical configuration that is shown to c orrespond to the maximum value of the determinant of the 6 x 6 Jacobia n matrix of the manipulator. This matrix is none other than that of th e normalized line coordinates of the six leg-lines; for its determinan t to be a maximum, the platform triangle is found to be half of the si ze of the base triangle, and the perpendicular distance between platfo rm and base is equal to the side of the platform triangle. When the ma nipulator is actuated so that the octahedron departs from this central configuration the determinant always diminishes, and, as is well know n, it becomes zero when a special configuration is reached (the platfo rm then gaining one or more uncontrollable freedoms). Our quality inde x lambda, 0 less than or equal to lambda less than or equal to 1, is a constructive measure of acceptable design proportions. The double-sph erical joints (there are six) are the source of the critical practical difficulties. Kinematic substitutions can circumvent this problem, bu t often there is no reasonable alternative to accepting a reduction of maximum quality index through separation by fairly short distances of some or all of the double-ball joints. Too great a separation easily leads too far toward generality; any fully-in-parallel manipulator of more general proportions should be tested for quality against our octa hedral form simply because no different form can be superior to a well -designed octahedron from the points of view of structural soundness a nd ability to apply both forces and controlled displacements to the en d-effector platform.