Shuguang Huang

Achieving an Arbitrary Spatial Stiffness with Springs Connected in Parallel

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.

The bounds and realization of spatial compliances achieved with simple serial elastic mechanisms

We address the spatial elastic behavior that can be achieved through the use of a serial chain of revolute and prismatic elastic joints. We show that, regardless of the number of joints or the configuration of the links, there exists a subspace within the 21-dimensional compliance matrix space that cannot be reached by a simple serial elastic mechanism. This restriction is shown to be dual to the restriction on the stiffness matrices associated with simple parallel mechanisms. Although analogous to each other, the two restrictions correspond to different elastic behaviors. A procedure to synthesize any realizable compliance matrix with a simple serial mechanism is provided. The dualities and differences between the parallel and serial cases are discussed.

The Duality in Spatial Stiffness and Compliance as Realized in Parallel and Serial Elastic Mechanisms

Spatial elastic behavior is characterized by a 6X6 positive definite matrix, the spatial stiffness matrix, or its inverse, the spatial compliance matrix. Previously, the structure of a spatial stiffness matrix and its realization using a parallel elastic system have been addressed. This paper extends those results to the analysis and realization of a spatial compliance matrix using a serial mechanism and identifies the duality in spatial stiffness and compliance associated with parallel and serial elastic mechanisms. We show that, a spatial compliance matrix can be decomposed into a set of rank-1 compliance matrices, each of which can be realized with an elastic joint in a serial mechanism. To realize a general spatial compliance, the serial mechanism must contain joints that couple the translational and rotational motion along/about an axis. The structure of a spatial compliance matrix can be uniquely interpreted by a 6-joint serial elastic mechanism whose geometry is obtained from the eigenscrew decomposition of the compliance matrix. The results obtained from the analysis of spatial compliant behavior and its realization in a serial mechanism are compared with those obtained for spatial stiffness behavior and its realization in a parallel mechanism.

Sufficient conditions used in admittance selection for force-guided assembly of polygonal parts

Admittance control approaches show significant promise in providing reliable force-guided assembly. An important issue in the development of these approaches is the specification of an appropriate admittance control law. This paper identifies procedures for selecting the appropriate admittance to achieve reliable force-guided assembly of planar polyhedral parts for single-point contact cases. A set of conditions that are imposed on the admittance matrix is presented. These conditions ensure that the motion that results from contact reduces part misalignment. We show that, for bounded misalignments, if an admittance satisfies the misalignment-reduction conditions at a finite number of contact configurations, then the admittance will also satisfy the conditions at all intermediate configurations.

A passive mechanism that improves robotic positioning through compliance and constraint

Abstract This paper presents the design of a passive robotic wrist that is capable of establishing and maintaining an accurate position relative to a workpart edge through compliance and constraint (force guidance). In previous work, we have shown that, through proper selection of a manipulators impedance, a manipulators end-effector can be guided to its desired relative position despite errors in its commanded position. The selected proper impedance is attained here through the design of a passive micromanipulator that is mounted on the end-effector of a conventional manipulator. The micromanipulator consists of three linkages connected by revolute joints and torsional springs. The outermost linkage contacts the workpart at multiple locations providing multidirectional unilateral kinematic constraint. This kinematic constraint in conjunction with the compliance provided by the torsional springs causes the linkage to be re-positioned so that any existing misalignment (that inevitably occurs) is eliminated and a unique planar position/orientation with respect to the workpart edge is attained. Here, we present the procedure used in the parametric design of this mechanism. The desired compliant properties identified in task space (using Cartesian variables ( x , y , and θ ) for force and motion) are extended here to joint space (using joint variables ( θ 1 , θ 2 ), and θ 3 ) for torque and motion). The appropriate micromanipulator link lengths, initial linkage angles, and the appropriate torsional spring constants are selected using an optimization procedure. Computer simulation of the constrained manipulator/workpart interaction demonstrates that the desired force guidance behavior is attained.

Admittance selection for force-guided assembly of polygonal parts despite friction

An important issue in the development of force guidance assembly strategies is the specification of an appropriate admittance control law. This paper identifies conditions to be satisfied when selecting the appropriate admittance to achieve force-guided assembly of polygonal parts for multipoint contact with friction. These conditions restrict the admittance behavior for each of the various one-point and two-point contact cases and ensure that the motion that results from contact reduces part misalignment for each case. We show that, for bounded friction and part misalignments, if the identified conditions are satisfied for a finite number of contact configurations and friction coefficients, the conditions ensure that force guidance is achieved for all configurations and values of friction within the specified bounds.

Sufficient conditions used in admittance selection for planar force-guided assembly

Admittance control approaches show significant promise in providing reliable force-guided assembly. An important issue in the development of these approaches is the specification of an appropriate admittance control law. This paper identifies procedures for selecting the appropriate admittance to achieve reliable planar force-guided assembly for single-point contact cases. A set of conditions that are imposed on the admittance matrix is presented. These conditions ensure that the motion that results from contact reduces part misalignment. We show that for bounded misalignment, if the conditions are satisfied for a finite number of contact configurations, the system ensures that force guidance is achieved for all intermediate configurations.

A Classification of Spatial Stiffness Based on the Degree of Translational–Rotational Coupling

Previously, we have shown that, to realize an arbitrary spatial stiffness matrix, spring components that couple the translational and rotational behavior along/about an axis are required. We showed that, three such coupled components and three uncoupled components are sufficient to realize any full-rank spatial stiffness matrix and that, for some spatial stiffness matrices, three coupled components are necessary. In this paper, we show how to identify the minimum number of components that provide the translational-rotational coupling required to realize an arbitrarily specified spatial stiffness matrix. We establish a classification of spatial stiffness matrices based on this number which we refer to as the degree of translational-rotational coupling (DTRC). We show that the DTRC of a stiffness matrix is uniquely determined by the spatial stiffness mapping and is obtained by evaluating the eigenstiffnesses of the spatial stiffness matrix. The topological properties of each class are identified. In addition, the relationships between the DTRC and other properties identified in previous investigations of spatial stiffness behavior are discussed.

Admittance selection for planar force-guided assembly for single-point contact with friction

This paper identifies procedures for selecting the appropriate admittance to achieve reliable planar force-guided assembly for single-point frictional contact cases. A set of conditions that are imposed on the admittance matrix is presented. These conditions ensure that the motion that results from contact reduces part misalignment. We show that, for bounded misalignments, if an admittance satisfies the misalignment-reduction conditions at a finite number of contact configurations and a given coefficient of friction /spl mu//sub M/) then the admittance will also ensure that the conditions are satisfied at all intermediate configurations for all coefficients less than /spl mu//sub M/.

Realization of Those Elastic Behaviors That Have Compliant Axes in Compact Elastic Mechanisms

In this article, we address the synthesis and realization of a subset of spatial elastic behaviors, those with compliant axes, in compact parallel mechanisms. Using the procedures developed, a geometric description of the layout of a compact mechanism of springs connected in parallel is obtained. In each of these mechanisms, each spring axis is restricted to intersect a single point in space. The variation in the orientation of the intersecting spring axes is also restricted. The degree of restriction in axis orientation is determined by the number of “compliant axes” associated with the specified elastic behavior. Also, as part of this work, a physical appreciation of the different classes of stiffnesses that have compliant axes is identified and interpreted in different types of concurrent parallel mechanisms.