This paper addresses manipulator admittance design with regard to reliable force guided assembly. Our goal is to design the admittance of the manipulator so that, at all possible part misalignments, the contact forces always lead to error-reducing motions. If this objective can be accomplished for a given set of parts, we call the parts force-assemblable.As a testbed application of manipulator admittance design for force guided assembly, we investigate the insertion of a workpiece into a fixture consisting of multiple rigid fixture elements (fixels). For reliable insertion, the fixture should have the property that contact with all fixels ensures a unique workpiece position (i.e., the fixture should be deterministic [Asada, 1985 #105]) and the property that contact with all fixels is ensured after the insertion motion terminates.Here, we define a linearly force-assemblable fixture to be one for which there exists an admittance matrix which necessarily results in workpiece contact with all fixels despite initial positional error. We show that, in the absence of friction, all deterministic fixtures are linearly force-assemblable. We also show how to design an admittance matrix that guarantees that the workpiece will be guided into the deterministic fixture by the fixel contact forces alone. IEEE Transactions . . . Schimmels, Peshkin: Force-Assemblability . . .

No abstract

In this paper, the synthesis of an arbitrary spatial stiffness matrix is addressed. We have previously shown that an arbitrary stiffness matrix cannot be achieved with conventional translational springs and rotational springs (simple springs) connected in parallel regardless of the number of springs used or the geometry of their connection. To achieve an arbitrary spatial stiffness matrix with springs connected in parallel, elastic devices that couple translational and rotational components are required. Devices having these characteristics are defined here as screw springs. The designs of two such devices are illustrated. We show that there exist some stiffness matrices that require 3 screw springs for their realization and that no more than 3 screw springs are required for the realization of full-rank spatial stiffness matrices. In addition, we present two procedures for the synthesis of an arbitrary spatial stiffness matrix. With one procedure, any rank-m positive semidefinite matrix is realized with m springs of which all may be screw springs. With the other procedure, any positive definite matrix is realized with 6 springs of which no more than 3 are screw springs.

If an admittance control law is properly designed, a workpiece can be guided into a fixture using only the contact forces for guidance (force-assembly). Previously, we have shown that: 1) a space of accommodation control laws that will ensure force-assembly without friction always exists, and 2) as friction is increased, a control law that allows force-assembly can be obtained as long as the forces associated with positional misalignment are characteristic. A single accommodation control law that allows force-assembly at the maximum value of friction can be obtained by an optimization procedure. The single accommodation control law obtained by the optimization procedure, however, is not unique. There exists a space of accommodation control laws that will allow force-assembly at, or below, the value of friction that marginally violates the characteristic forces condition. Here, for the purpose of the accommodation control law design, a set of linear sufficient conditions is used to generate accommodation basis matrices. Any nonnegative linear combination of the accommodation basis matrices that, when combined, yields a positive definite accommodation matrix is guaranteed to provide force-assembly at or below a specified value of friction. (Basis matrices exist only if that specified value of friction is less than the value for which forces are still characteristic.) 1.0 Introduction This work addresses one of the most basic current limitations of automated assembly: the failure of an assembly task when part relative positional misalignment occurs. In automated assembly,

Force-assembly has been defined as an assembly process for which the use of a single, properly designed, admittance control law will guarantee the proper assembly of a given pair of mating parts. In previous work in workpart-intofixture insertion, the conditions on a manipulator's accommodation control law that ensure proper insertion despite infinitesimal positional error and finite (but bounded) friction have been identified. Through the use of an optimization routine, a control law that satisfies these force-assembly conditions at or below a friction maximum value can be obtained. This single control law, however, is not unique-there exists many other control laws that will satisfy the conditions of force-assembly at the same value of friction. This paper addresses the identification and construction of a linear space of accommodation control law parameters that ensure force-assembly with friction. First, linear sufficient conditions that ensure force-assembly with friction are identified. These linear sufficient conditions are then modified to separate the N 2 +N dimensional space of accommodation control law parameters into N +1 different N-dimensional subspaces. A means of efficiently generating basis nominal velocity vectors and basis accommodation matrices is presented. A nominal velocity selected using any positive linear combination of the nominal velocity basis vectors and an accommodation matrix selected using any positive linear combination of the accommodation basis matrices will guarantee force-assembly (for any value of friction less than that used in generating the basis matrices). A planar example of the construction of each accommodation control law subspace is presented and illustrated in the geometry of the fixturing task.