On the design of the kinematic structure of seven-axes redundant manipulators for maximum conditioning

Abstract

The kinematic design of redundant seven-axis manipulators is addressed. It is shown that isotropic seven-axis manipulators are possible. Three different optimum solutions are presented: first, a nonlinear minimization problem is solved which, in effect, renders the Jacobian matrix fully isotropic. Next, it is argued that, despite the fully isotropic feature of the first solution, some of its structural features can be improved. This leads to pre-assigning some of the parameters defining the structure of the manipulator, resulting in a system of 21 nonlinear equations in 21 unknowns. As the second solution, the Hartenberg-Denavit parameters of an isotropic manipulator are then obtained by solving the said system of nonlinear equations. Further constraints to make the manipulator structure anthropomorphic yield a third solution. This last solution gave rise to a manipulator which is not fully isotropic but is very close to isotropy, and exhibits a greater resemblance to the structure of the human arm.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>