The Kinetostatic Conditioning of Two-Limb Schönflies Motion Generators

This paper introduces a study on the kinetostatic conditioning of two-limb Schönflies motion generators. These are robots capable of producing the motions undergone by the end-effector of what is known as selective-compliance assembly robot arm (SCARA) systems, which can best be described as the motions of the tray of a waiter: three independent translations plus one rotation about an axis of fixed orientation. SCARA systems are usually understood as four-axis serial robots, Schönflies motion generators being a generalization thereof, that encompass first and foremost parallel architectures. Kinetostatic conditioning is understood here in connection with the condition number of each of the two Jacobian matrices of the parallel robot under study. After a brief introduction on the geometry and the kinematics of two-limb parallel systems, the kinetostatics of this class of robots is discussed; whence, the calculation of the kinetostatic conditioning of these robots is undertaken. The motivation behind this work is the need to understand an unstable behavior of the prototype in a substantial part of its workspace, which is attributed to poor conditioning. A main result of this paper is the correlation between the shortest dimension of the robot kinematic chain and the characteristic length, which hints to the need of specifying the range of the characteristic length when optimizing the dimensions of robots of the class studied here, a result that may equally hold for parallel robots in general.