perm filename ABSTR.ROM[NET,GUE] blob sn#877473 filedate 1989-09-21 generic text, type T, neo UTF8

ABSTRACT for ROMANSY-90 A General Solution for the Inverse Kinematics of All Series Chains Dr. Madhusudan Raghavan Prof. Bernard Roth General Motors Research Laboratories and Dept. of Mech. Eng. Warren, Michigan, USA Stanford University Stanford, CA 94305, USA The inverse kinematics problem is the name given to the problem of determining those joint coordinates for a manipulator for which its end-effector takes on a desired position and orientation. It is known that, for a general manipulator geometry, a manipulator with 6 revolute joints (a 6R) can have at most 16 sets of joint coordinates corresponding to a single end-effector position and orientation. Recently we, as well as other researchers, have been able to reduce the inverse kinematics problem for a 6R manipulator to a single polynomial of degree 16 in one of the joint-angle variables. Our paper describing these results was present at the ISRR meeting in Tokyo this August, it is titled "Kinematic Analysis of the 6R Manipulator of General Geometry." What we proposed for ROMANSY is to show that the elimination techniques that were developed for the 6R are in fact universally applicable to any series chain. The argument goes as follows: first, we restrict ourselves to 6-degree-of-freedom chains with any combination of revolute and 3 or less prismatic joints. In this case we go through all the possibilities in this paper and show the reader exactly which variables need to be eliminated, how to do it, and in which cases the resultant polynomial will have degree less than 16. Our results include the well known fact that if 3 adjacent revolute axes intersect we get a polynomial of degree 8. Second, we show that anytime we have less than 6-degrees-of-freedom or more than 3 prismatic joints, the result follows trivially from the above by simply setting certain values to zero or some other convenient numerical value. Third, we mention that any system with more than 6-degrees-of-freedom allows for arbitrary choices which reduces the problem to one of the 6-degree-of-freedom problems we have solved. Finally we mention that any type of lower pair joint can be represented as a combination of revolute and prismatic joints. For these reasons we can claim our analysis is universal for any combination of lower pair joints arranged in series. The heart of this paper will be the material mentioned as the first point in the foregoing. All the other arguments are very short and obvious. For the first point, we will be presenting new results that show that the original set of closure equations may be supplemented by an additional set of equations which lie in the ideal of the closure set and have exactly the same number of power products as the set of closure equations. This new set of equations together with the original form the basis group from which we can obtain a single polynomial using the method of dyalitic elimination. It will be shown that in every case our resultant polynomial is of exactly the minimum degree and contains no extraneous solutions. ≠