Waseem A. Khan

The Kinetostatic Optimization of Robotic Manipulators: The Inverse and the Direct Problems

The design of a robotic manipulator begins with the dimensioning of its various links to meet performance specifications. However, a methodology for the determination of the manipulator architecture, i.e., the fundamental geometry of the links, regardless of their shapes, is still lacking. Attempts have been made to apply the classical paradigms of linkage synthesis for motion generation, as in the Burmester Theory. The problem with this approach is that it relies on a specific task, described in the form of a discrete set of end-effector poses, which kills the very purpose of using robots, namely, their adaptability to a family of tasks. Another approach relies on the minimization of a condition number of the Jacobian matrix over the architectural parameters and the posture variables of the manipulator. This approach is not trouble-free either, for the matrices involved can have entries that bear different units, the matrix singular values thus being of disparate dimensions, which prevents the evaluation of any version of the condition number. As a means to cope with dimensional inhomogeneity, the concept of characteristic length was put forth. However, this concept has been slow in finding acceptance within the robotics community, probably because it lacks a direct geometric interpretation. In this paper the concept is revisited and put forward from a different point of view. In this vein, the concept of homogeneous space is introduced in order to relieve the designer from the concept of characteristic length. Within this space the link lengths are obtained as ratios, their optimum values as well as those of all angles involved being obtained by minimizing a condition number of the dimensionally homogeneous Jacobian. Further, a comparison between the condition number based on the two-norm and that based on the Frobenius norm is provided, where it is shown that the use of the Frobenius norm is more suitable for design purposes. Formulation of the inverse problem—obtaining link lengths—and the direct problem—obtaining the characteristic length of a given manipulator—are described. Finally a geometric interpretation of the characteristic length is provided. The application of the concept to the design and kinetostatic performance evaluation of serial robots is illustrated with examples.

Kinetostatic Design of an Innovative Schönflies-Motion Generator

Abstract In this paper, a novel parallel robot is introduced. The robot, a Schönflies-motion generator (SMG), is capable of a special class of motions, namely those produced with serial robots termed SCARA (selective-compliance assembly robot arm). These motions involve three independent translations and one rotation about an axis of fixed direction. Such motions are known to form a subgroup of the displacement group of rigid-body motions, termed the Schönflies subgroup. The SMG is composed of two identical four-degree-of-freedom serial chains in a parallel array, sharing one common base and one common moving platform. The proximal module of each chain is active and has two controlled axes, the motors being installed on the fixed base. The links can thus be made light, thereby allowing for higher operational speeds. The distal module, in turn, is passive and follows the motions of its active counterpart, the whole mechanism giving, as a result, a four-degree-of-freedom motion to its end platform.

Recursive Kinematics and Inverse Dynamics for a Planar 3R Parallel Manipulator

We focus on the development of modular and recursive formulations for the inverse dynamics of parallel architecture manipulators in this paper. The modular formulation of mathematical models is attractive especially when existing sub-models may be assembled to create different topologies, e.g., cooperative robotic systems. Recursive algorithms are desirable from the viewpoint of simplicity and uniformity of computation. However, the prominent features of parallel architecture manipulators-the multiple closed kinematic loops, varying locations of actuation together with mixtures of active and passive joints-have traditionally hindered the formulation of modular and recursive algorithms. In this paper, the concept of the decoupled natural orthogonal complement (DeNOC) is combined with the spatial parallelism of the robots of interest to develop an inverse dynamics algorithm which is both recursive and modular. The various formulation stages in this process are highlighted using the illustrative example of a 3R Planar Parallel Manipulator.

A Novel Paradigm for the Qualitative Synthesis of Simple Kinematic Chains Based on Complexity Measures

Proposed in this paper is a paradigm for the qualitative synthesis of simple kinematic chains that is based on the concept of complexity. Qualitative synthesis is understood here as the number and the type stages of the kinematic-synthesis process. The formulation hinges on the geometric complexity of the surface associated with lower kinematic pairs. First, the geometric complexity of curves and surfaces is recalled, as defined via the loss of regularity (LOR). The LOR, based in turn on the concept of diversity, measures the spectral richness of the curvature of either the curve or the surface under study. The paper closes with a complexity analysis of all six lower kinematic pairs, as a means to guide the mechanical designer into the conceptual stage of the design process. The paradigm is illustrated with the computation of the complexity of the four-bar linkage in all its versions, planar, spherical, and spatial, as well as that of a transmission for the conversion of a rotation about a vertical axis into one about a horizontal axis.

Complexity analysis for the conceptual design of robotic architecture

We propose a formulation capable of measuring the complexity of kine- matic chains at the conceptual stage in robot design. As an example, two realizations of the Schonflies displacement subgroup are compared.

Recursive Kinematics and Inverse Dynamics for Parallel Manipulators

We examine here the modular and recursive formulation of the inverse dynamics of parallel architecture mainpulators. The concept of the decoupled natural orthogonal complement (DeNOC) is combined with the spatial parallelism of the robots of interest to develop an inverse dynamics algorithm which is both recursive and modular.Copyright