K.H. Hunt

Kinematic chains for robot hands—I. Orderly number-synthesis

Abstract Number synthesis of kinematic chains usually involves the generation of a complete list of kinematic chains followed by a time-consuming, computer-intensive procedure for the elimination of isomorphs. A significant unsolved problem in number synthesis is the guaranteed precise elimination of all isomorphs. Since there is no efficient algorithm for always determining whether two kinematic chains are isomorphic, any “efficient” algorithm has a finite probability of rejecting a unique, potentially useful, chain. This paper reviews the history of number synthesis and presents a new orderly method for synthesising kinematic chains. This new Melbourne method guarantees to produce a complete list of chains, which, only when some doubt to the uniqueness of a chain exists, may include an isomorphic chain. As a consequence, this technique produces significantly fewer isomorphs in the output list than do previous techniques; often no isomorphs are produced by the method whatsoever. It is proposed that in many situations where the synthesis of kinematic chains is required, the processing of duplicate chains in the early stage of design is preferable to the omission of a potentially useful chain.

The Octahedral Manipulator: Geometry and Mobility:

In most of the practical six-actuator, in-parallel manipulators, the octahedral form is either taken as it stands or is approximated. Yet considerable theoretical attention is paid in the literature to more general forms. Here we touch on the general form, and describe some aspects of its behavior that vitiate strongly against its adoption as a pattern for a realistic manipulator. We reach the conclusion that the structure for in-parallel manipulators must be triangulated as fully as possible, so leading to the octahedral form. In describing some of the geometrical properties of the general octahedron, we show how they apply to manipulators. We examine in detail the special configurations at which the 6 x 6 matrix of leg lines is singular, presenting results from the point of view of geometry in preference to analysis. In extending and enlarging on some known properties, a few behavioral surprises materialize. In studying special configurations, we start with the most general situation, and every other case derives from this. Our coverage is more comprehensive than any that we have found. We bring to light material that is, we think, of significant use to a designer.

Special configurations of multi-finger multi-freedom grippers—a kinematic study

Screw theory is used to establish the general kinematic prin ciples offully-in-series and fully-in-parallel devices. Through screw theory, we show that a workpiece grasped by a fully-in- series manipulator can only lose freedom while a workpiece grasped by a fully-in-parallel manipulator can only gain freedom. Multi-finger multi-freedom grippers or robot hands use a mixture of in-parallel and serial actuation, and so a workpiece grasped by such a device can both gain and lose freedom. These linkages belong to a class called composite serial/in-parallel manipulators. Using the well-established concepts of screw systems and reciprocity, we identify the general criteria that govern the gain and loss of workpiece freedoms. We illustrate how these gains and losses of work piece freedom arise, by considering the Stanford/JPL hand.

Identification of the Special Configurations of the Octahedral Manipulator using the Pure Condition

This paper presents a technique, known as the Pure Condition, which has found use in analysing the rigidity of truss-like structures. The analysis is applied to the Stewart Platform where it can be used to identify special configurations. The conditions that produce special configurations in the octahedral manipulator are compared to previously known conditions and the associated geometry is seen to be more revealing with this method than was the case previously. The results lead to a simple and clear method for identifying special configurations in the octahedral manipulator and other specializations of the Stewart Platform.

Unifying screw geometry and matrix transformations

Transformation matrices are widely used in robotics for kinematic analysis and trajectory planning. Screw geome try offers better geometric insight into such analyses. In this article we unify the two approaches through the use of invariant properties of orthogonal matrices under simi larity transformations. We give a complete expression for the finite screw motion in terms of the entires of a 3 x 3 dual-number transformation matrix. Our analysis suggests that the finite screw is suitable for trajectory planning, and we develop a concise expression that gives the trans formation matrix describing the displacement at each point along the path of the finite screw motion.

Kinematic chains for robot hands. II: Kinematic constraints, classification, connectivity, and actuation

The work in this paper follows on from Part 1. We now consider the specific example of robot hands and identify several kinematic constraints of these devices. The method for number synthesis of kinematic chains in Part 1 is applied in several different ways in order to synthesise chains suitable for application as robot hands; several examples of the structures so found are presented. So as to identify those kinematic chains that are more promising than others, the new concept of minimal sets of kinematic chains is defined. Another new concept, the variety of a kinematic chain, is defined and used to make generalisations about relative connectivity within kinematic chains, which has application in the selection of actuated pairs. Fractionation of kinematic chains is reviewed in light of the concept of variety. The work presented here has application far beyond the number synthesis of alternative structures for robot hands.

Finite displacements of points, planes, and lines via screw theory

Abstract Geometrical elements, namely point, directed plane, and directed line, are here taken in isolation from any rigid body to which they may belong. The available finite screws are fully determined for a general finite displacement of each element. Each screw carries a quasi-pitch, or “quatch”, that reduces to the commonly-accepted pitch when a displacement becomes infinitesimal. Each element-displacement has its “quatched” screw system, that for the line displacement being quadratic. The quatched screw systems then intersect in twos for displacements of point-line, plane-line, and point-plane combinations, to reveal quatched linear two-systems. Finally the triple combination point-plane-line yields a single finite quatched screw. Applications in robotics are touched upon.

A dexterity measure for the kinematic control of a multifinger, multifreedom robot hand

This work examines the properties of the manifold gener ated as the configuration space of the linkage used for each finger of the Salisbury hand. We begin with an exhaustive catalog of design types for the finger based on an analysis of its branch loci. We then study the condi tions under which the forward kinematic map becomes singular. These singularities define a submanifold that partitions the linkages configuration space into a number of open sheets, each of which maps diffeomorphically onto a corresponding open region in the fingers reach able work space. Next we consider the determinant func tion of the fingers Jacobian matrix. The stationary points of this function reveal those configurations where the Jacobian determinant is a maximum. The Jacobian deter minant can be thought of as an oriented volume in the tangent space to the fingers work space, and the orienta tion of this volume reveals the most favorable direction(s) for effecting tip motion or, reciprocally, for applying tip forces. From this we establish a simple criterion that can be used to find the optimal grasp configuration(s) for a given finite displacement of the workpiece.

On Optimizing the Kinematic Geometry of a Dextrous Robot Finger

Building on previous work, where we identified kinematic chains suitable for application as dextrous robot hands, we now explore how to optimize the kinematic geometry of a multiloop, multifree dom mechanism so that simple equations of movement are achieved. Specifically, we wish to find the mechanism geometry that provides the simplest expressions for the movement of the fingertip. Being based in geometry, the approach described here is applicable to a wide range of mechanism-design problems.

A spatial extension of Cardanic movement: its geometry and some derived mechanisms

In planar Cardanic movement a body is constrained by making two of its points lie on two coplanar lines. This paper provides a spatial extension to planar Cardanic movement, where the two straight lines (directrices), on which two points of the body are guided, are no longer coplanar, and the body is free to spin out of planar motion. Our aim is to determine the movement of a general point of the moving body. We derive an algebraic surface and, by examining its properties, develop some mechanisms that derive from this generalized Cardanic movement. We also examine all the degenerate and special cases of general Cardanic movement. This work provides insight into the design of certain mechanisms, and explains some apparently discrepant results.