Instantaneous kinematics and singularity analysis of three-legged parallel manipulators

Abstract

Instantaneous kinematics and singularity analysis of a class of three-legged, 6-DOF parallel manipulators are addressed in this paper. A generic method of derivation of reciprocal screw and consequently, the instantaneous kinematics model is presented. The advantage of this formulation is that the instantaneous kinematics model possesses well-defined geometric meaning and algebraic structure. Singularity analysis is performed under three categories, namely forward, inverse and combined singularities. A new concept of Passive Joint Plane is introduced to correlate the physical structure of the manipulator and these geometric conditions. In the inverse kinematic analysis, a new approach is introduced. At each leg end point a characteristic parallel- epiped is defined whose sides are the linear velocity components from three main joints of the leg. An inverse singularity occurs when the volume of this parallelepiped becomes zero. Examples are demonstrated using RRRS and RPRS-type parallel manipulators.

A Formal-Numerical Approach for Robust In-Workspace Singularity Detection

“…Natural evaluation may be simply illustrated with when lies in the range [3,5]. In that case, we can safely state that, for any instance of in [3,5], then lies in [9,25], in [6,10] and, consequently, lies in . Summing the interval for and leads to , which constitutes the interval evaluation of over the range [3,5].…”

Comparison between 3 and 8 Leg 6-DOF shake table

“…and for six actuator (RPRS, alternative design) shake table of 670mm height is used in calculation of stiffness matrix. Stiffness analysis of parallel manipulators is done using the concept of twist generator and twist annihilator [9,10]. Various co-ordinates are designated for both designs and are used in the equations obtained in calculation for stiffness matrix.…”

“…Stiffness matrix K = k i .J T .J [9,10] is 6×6 matrix, here k i is stiffness constant of i th joint actuator and is J = B -1 .A. …”

A Six Degree of Freedom Epicyclic-Parallel Manipulator

“…Three-legged six-dof manipulators were introduced to overcome this workspace limitation and do not suffer from the same limb interference as their six-legged counterparts [16]. However, to achieve six-dof with only three legs requires actuators to be mounted on the moving limbs, thus increasing the mass and inertia of the moving parts.…”