A force–torque sensor based on a Stewart Platform in a near-singular configuration

THE vector analysis of Gibbs and Heaviside and the more general tensor analysis of Ricci are now recognized as standard tools in mechanics, hydro-dynamics and electrodynamics. Their use not only materially simplifies and condenses the exposition, but also makes mathematical concepts more tangible and easy to grasp. Moreover, tensor analysis provides a simple automatic method for constructing invariants. Since a tensor equation has precisely the same form in all co-ordinate systems, the desirability of stating physical laws or geometrical properties in tensor form is manifest. The perfect adaptability of the tensor calculus to the theory of relativity was responsible for its original renown. It has since won a firm place in mathematical physics and engineering technology. Thus Sir Edmund Whittaker rates the tensor calculus as one of the three principal mathematical advances in the last quarter of the nineteenth century. Vector and Tensor Analysis By Prof. Louis Brand. Pp. xvi + 439. (New York: John Wiley and Sons, Inc.; London: Chapman and Hall, Ltd., 1947.) 33s. net.

Vector and Tensor Analysis

Prediction of the pose errors produced by joints clearance for a 3-UPU parallel robot

Example embodiments may relate to methods and systems for selecting a grasp point on an object. In particular, a robotic manipulator may identify characteristics of a physical object within a physical environment. Based on the identified characteristics, the robotic manipulator may determine potential grasp points on the physical object corresponding to points at which a gripper attached to the robotic manipulator is operable to grip the physical object. Subsequently, the robotic manipulator may determine a motion path for the gripper to follow in order to move the physical object to a drop-off location for the physical object and then select a grasp point, from the potential grasp points, based on the determined motion path. After selecting the grasp point, the robotic manipulator may grip the physical object at the selected grasp point with the gripper and move the physical object through the determined motion path to the drop-off location.

Object Pickup Strategies for a Robotic Device

The aim of this paper is two-fold: first, it provides an overview of the implementation of Grassmann-Cayley algebra to the study of singularities of parallel robots1 and, second, this algebra is utilized to solve the singularity of a general class of Gough-Stewart platforms (GSPs). The Grassmann-Cayley algebra has an intuitive way of representing geometric entities and writing them and their incidence algebraically. The singularity analysis is performed using the bracket representation of the Jacobian matrix determinant associated with this algebra. This representation is a coordinate-free one, and for all cases treated and addressed in this paper, it enables the translation of the algebraic expression into a geometrically meaningful statement. The class of GSPs having two pairs of collocated joints, whose singularity is treated in this paper, is one of the more general classes. Their singularity analysis and geometrical interpretation, is presented here, to the best of our knowledge, for the first time.

Sandipan Bandyopadhyay

Papers

Analysis of configuration space singularities of closed-loop mechanisms and parallel manipulators

Geometric characterization and parametric representation of the singularity manifold of a 6–6 Stewart platform manipulator

An algebraic formulation of kinematic isotropy and design of isotropic 6-6 Stewart platform manipulators

Analytical determination of principal twists in serial, parallel and hybrid manipulators using dual vectors and matrices

Dynamic singularity avoidance for parallel manipulators using a task-priority based control scheme