This paper presents a critical analysis of the metric of rigid body displacements obtained from the so-called kinematic mapping. It is shown that this metric is not suitable for finite rigid bodies. The paper also addresses the metrics obtained for the planar group, as it can be regarded as a subgroup of the group of all rigid body displacements, which is denoted here as the Euclidean group. Finally, the paper proposes some metrics for the set of spatial and planar displacements for a finite rigid body, undergoing a finite displacement.

On the Metrics of Rigid Body Displacements for Infinite and Finite Bodies

Single Degree-of-freedom Coupled Serial Chain (SDCSC) mechanisms form a novel class of modular and compact mechanisms with a single degree-of-freedom, suitable for a number of manipulation tasks. Such SDCSC mechanisms take advantage of the hardware constraints between the articulations of a serial-chain linkage, created using gear-trains or belt/pulley drives, to guide the end-effector motions and forces. In this paper, we examine the dimensional synthesis of such SDCSC mechanisms to perform desired planar manipulation tasks, taking into account task specifications on both end-effector motions and forces. Our solution approach combines precision point synthesis with optimization to realize optimal mechanisms, which satisfy the design specifications exactly at the selected precision points and approximate them in the least-squares sense elsewhere along a specified trajectory. The designed mechanisms can guide a rigid body through several positions while supporting arbitrarily specified external loads. Furthermore, torsional springs are added at the joints to reduce the overall actuation requirements and to enhance the task performance. Examples from the kinematic and the kinetostatic synthesis of planar SDCSC mechanisms are presented to highlight the benefits.

Kinematic and Kinetostatic Synthesis of Planar Coupled Serial Chain Mechanisms

This paper presents a kinematic procedure to synthesize planar mechanisms, composed of rigid links and revolute joints, capable of approximating a shape change defined by a set of curves. These "morphing curves", referred to as design profiles, differ from each other by a combination of rigid-body displacement and shape change. Design profiles are converted to piecewise linear curves, referred to as target profiles, that can be readily manipulated. In the segmentation phase, the geometry of rigid links that approximate the shapes of corresponding segments from each target profile is determined. In the mechanization phase, these rigid links are joined together at their end points with revolute joints to form a single chain. Dyads are then added to reduce the number of degrees of freedom (DOF's) to any desired value, typically 1. The approach can be applied to any number of design profiles that can be approximated with any number of rigid links, which can then be used to construct a mechanism with any number of DOF's. Naturally, greater difficulty is encountered for larger numbers of design profiles and/or links and for more dramatic changes in shape. The procedure is demonstrated with examples of single-DOF mechanisms approximating shape changes between two and three design profiles.

Kinematic Synthesis of Planar, Shape-Changing Rigid-Body Mechanisms

DESIGN AND VIRTUAL PROTOTYPING OF USER-CUSTOMIZED ASSISTIVE DEVICES Venkat Narayan Krovi Vijay Kumar and G. K. Ananthasuresh The focus of this dissertation is on the design, virtual prototyping and physical realization of one-of-a-kind assistive devices that are physically coupled or attached to the human user. This class of articulated assistive devices called teletheses are designed to be passive. The intimate physical coupling enables their use as \extensions" powered by the remaining functional musculature of the partially disabled user. The novel class of Coupled Serial Chains (CSC) mechanisms is used in the design of such teletheses. CSC mechanisms can be realized by physically coupling the various joint rotations of a serial chain robotic device using cable and pulley drives. The resulting devices retain the serial-chain con guration but have fewer degrees of freedom. Their simplicity makes them highly suitable for actuation and control of complex position-force tasks by human users. Task-speci c customization of such CSC mechanisms is necessary to enhance task performance. This is accomplished by design in the framework of dimensional synthesis of mechanisms. The main contributions of this dissertation are: 1. A modular integrated design environment, combining tools from synthesis, simulation and optimization with visualization to aid early user-customization and rapid design realization. 2. Optimal design of planar and spatial single degree-of-freedom coupled serial chain (SDCSC) mechanisms for matching desired end-e ector position and force task speci cations by combining precision point synthesis with optimization. Speci cally, we highlight the systematic formulation and analytic solution of precisionpoint path synthesis equations for 2-link spatial SDCSC mechanisms; and the kinetostatic design of SDCSC mechanisms to trace desired end-e ector trajectories while supporting arbitrary loads, with and without torsional springs at the revolute joints. The method for developing one-of-a-kind products is illustrated with a case study of a user-customized head controlled feeding aid for quadriplegics. vi

Design and virtual prototyping of user-customized assistive devices

This paper presents a unified approach to the problem of dimensional synthesis of the five-link, four-link, and three-link (double-wishbone) suspension mechanisms with a rack-and-pinion steering in...

A unified approach to the kinematic synthesis of five-link, four-link, and double-wishbone suspension mechanisms with rack-and-pinion steering control:

Y. L. Sarkisyan

Papers

Kinematic Geometry Associated With the Least-Square Approximation of a Given Motion

Chebychev Approximations of Finite Point Sets with Application to Planar Kinematic Synthesis

Chebychev Approximations of Spatial Point Sets Using Spheres and Planes