Kinematic manipulability of general constrained rigid multibody systems

Abstract

Abstract-This paper extends the kinematic manipulability concept commonly used for serial manipulators to general constrained rigid multibody systems. Examples of such systems include multiple cooperating manipulators, multiple fingers holding a payload, multileg walking robots, and variable geometry trusses. Explicit formulas for velocity and force manipulability ellipsoids are derived and their duality explained. Singularities are classified into two types: 1) unmanipulable singularity; 2) unstable singularity. The former is similar the singularities in serial chains where velocity manipulability ellipsoid is degenerate and force manipulability ellipsoid infinite. The latter is unique to parallel mechanisms, the velocity manipulability ellipsoid becomes infinite and force manipulability degenerate. In the case of multifinger grasp, these concepts correspond to unmanipulable or unstable grasps.

Kinematic control of constrained robotic systems

“…The definitionθ p = w andθ a =θ allow us to represent the system in a more generally form, according to (5) and (6), by means of (Wen and Wilfinger, 1999) …”

“…Some examples of other types of contacts and associated values of the selection matrix H are presented in (Murray et al, 1994;Wen and Wilfinger, 1999).…”

“…Typical examples include: deburring, contour following, grinding, machining, painting, polishing and object aligning (Namvar and Aghili, 2005) or even robot dexterous hands (Caurin and Pedro, 2009). In this framework, a study of the differential kinematics and manipulability indexes for multiple cooperating robot arms with unactuated joints is presented in (Wen and Wilfinger, 1999;Bicchi and Prattichizzo, 2000). Advanced motion and force control of cooperative robotics manipulators with passive joint are considered in (Tinos et al, 2006;Pazelli et al, 2011).…”

Quantifying and Optimizing Failure Tolerance of a Class of Parallel Manipulators

“…Gough Stewart Platforms are a classic example of manipulators belonging to this class. On the contrary, in multi-fingered grasps, the impact of failures on the kinematic representation is a function of composite manipulability Jacobian matrix, described in (Wen & Wilfinger, 1999) and cannot be directly derived by elimination of rows or columns. The mechanisms treated in this work belong to the former class, which will be characterized by " # J .…”

Rapid Prototyping of Overhead Crane Dynamics for Operation Use

“…This should be preceded by cause-effect analysis carried out on a group of the devices of the same class and working in the similar conditions, or on the virtual models of such devices. Today more and more interest in device modelling and simulation area has been shown towards multibody dynamics (Geradin et al, 2001;Bauchau, 1998;Murphy et al, 1993;Wen, 1999).…”