Sufficient Conditions for Admittance to Ensure Planar Force-assembly in Multi-point Frictionless Contact

An important issue in the development of force guidance assembly strategies 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 multi-point contact cases. Conditions that restrict the admittance behavior for each of the various types of two-point contact are presented. These conditions ensure that the motion that results from contact reduces part misalignment for each case. We show that, for bounded misalignments, if the conditions are satisfied for a finite number of contact configurations, the conditions ensure that force guidance is achieved for all configurations within the specified bounds

Admittance Selection for Force-guided Assembly of Polyhedral Parts in Single-point Contact

The selection of the proper admittance is important in achieving force-guided assembly. This paper identifies procedures for selecting the appropriate spatial admittance to achieve reliable force-guided assembly of polyhedral parts for single-point frictionless contact cases. Sets of conditions that are imposed on the admittance matrix for different types of single-point contact are presented. These conditions ensure that the motion that results from contact reduces part misalignment in the selected contact state. We show that, for bounded misalignments, if an admittance satisfies the misalignment-reduction conditions at a finite number of contact configurations, then the admittance also satisfy the conditions at all intermediate configurations

A Mass-Spring-Damper Model of a Bouncing Ball

The mechanical properties of a vertically dropped ball, represented by an equivalent mass-spring-damper model, are shown to be related to impact parameters. In particular, the paper develops relationships connecting the mass, stiffness and damping of a linear ball model to the coefficient of restitution and the contact time of the ball with the surface during one bounce. The paper also shows that the ball model parameters are functions of quantities readily determined in an experiment: (i) the height from which the ball is dropped from rest, (ii) the number of bounces, and (iii) the time elapsing between dropping the ball and the ball coming to rest. For a ball with significant bounce, approximate expressions are derived for the model parameters as well as for the natural frequency and damping ratio. Results from numerical and experimental studies of a bouncing ping-pong ball are presented

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/

Comments on “The Principal Axes Decomposition of Spatial Stiffness Matrices”

A significant amount of research has been directed toward developing a more intuitive appreciation of spatial elastic behavior. Results of these analyses have been described in terms of behavior decompositions and in terms of behavior centers. In a recent paper entitled “The Principal Axes Decomposition of Spatial Stiffness Matrices” by Chen et al. (IEEE Trans. Robot., vol. 31, no. 1, pp. 191-207), a decomposition of spatial stiffness was presented, and centers of stiffness and compliance were identified. The results presented in the paper have substantial overlap with previously published results and redefine previously used terms. The objective of this communication is to clarify the contributions of prior work and to standardize the terminology used in describing spatial elastic behavior

Geometric Construction-Based Realization of Spatial Elastic Behaviors in Parallel and Serial Manipulators

This paper addresses the realization of spatial elastic behavior with a parallel or a serial manipulator. Necessary and sufficient conditions for a manipulator (either parallel or serial) to realize a specific elastic behavior are presented and interpreted in terms of the manipulator geometry. These conditions completely decouple the requirements on component elastic properties from the requirements on mechanism kinematics. New construction-based synthesis procedures for spatial elastic behaviors are developed. With these synthesis procedures, one can select each elastic component of a parallel (or serial) mechanism based on the geometry of a restricted space of allowable candidates. With each elastic component selected, the space of allowable candidates is further restricted. For each stage of the selection process, the geometry of the remaining allowable space is described

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 Mass-Spring-Damper Model of a Bouncing Ball (Conference proceeding)

The mechanical properties of a vertically dropped ball, represented by an equivalent mass-spring-damper model, are related to the coefficient of restitution and the time of contact of the ball during one bounce with the impacting surface. In addition, it is shown that the coefficient of restitution and contact time of a single bounce are related to the total number of bounces and the total time elapsing between dropping the ball and the ball coming to rest. For a ball with significant bounce, approximate expressions for model parameters, i.e., stiffness and damping or equivalently natural frequency and damping ratio, are developed. Experimentally based results for a bouncing pingpong ball are presented

Realization Of Point Planar Elastic Behaviors Using Revolute Joint Serial Mechanisms Having Specified Link Lengths

This paper presents methods for the realization of 2 × 2 translational compliance matrices using serial mechanisms having only revolute joints, each with selectable compliance. The link lengths of the mechanism and the location of the compliant frame relative to the mechanism base are arbitrary but specified. The realizability of a given compliant behavior is investigated, and necessary and sufficient conditions for the realization of a given compliance with a given mechanism are obtained. These realization conditions are interpreted in terms of geometric relationships among the joints. We show that, for an appropriately sized 3R serial mechanism, any single 2 × 2 compliance matrix can be realized by properly choosing the joint compliances and the mechanism configuration. Requirements on mechanism geometry to realize every particle planar elastic behavior at a given location just by changing the mechanism configuration are also identified