A Class of Parallel Manipulators Based on Kinematically Simple Branches

Abstract

Parallel manipulators consisting of serial branches acting in parallel on a common end effector are examined. All nonredundant, six DOF manipulators corresponding to this in-parallel class of structures are enumerated. A specific in-parallel structure, three branches with two actuated joints per branch (3–2,2,2), is chosen as most promising based upon performance considerations. A class of kimematically simple (KS) serial-chain branch joint layouts suitable for the chosen in-parallel structure is defined. Arguments based upon kinematic equivalency of the branches and mobility of the assembled in-parallel manipulator chain are used to show that there exist only five unique branch joint-layouts belonging to the KS class. It is demonstrated that the solution to the inverse displacement problem for in-parallel manipulators based on the KS branches can be expressed in a closed form. Furthermore, the 3–2,2,2 in-parallel manipulators are shown to belong to a family of manipulators whose forward displacement solutions can be resolved through roots of a 16th order polynomial.

Semi-numerical solution to 6/6-Stewart-platform kinematics based on symmetry

“…Dexterity may for example be defined as the condition number of the Jacobi matrix. Refer to [25], [30], [26], or [22] for design considerations of Stewart-platform type architectures. …”

Error Analysis and Experimental Study of a Bi-Planar Parallel Mechanism in a Pedicle Screw Robot System

“…The accuracy of the parallel mechanisms has been investigated in [9,10,11,12]. Like in traditional machine tools, there are several major factors that influence the precision of parallel mechanisms; the main errors are as follows [13]: (1) Original manufacturing errors; (2) assembly errors; (3) errors resulting from distortion caused by force and heat; (4) control system errors and actuator errors and (5) other stochastic errors [14].…”

Design of a reconfigurable planar parallel manipulator

“…Podhorodeski and Nokleby 5 presented the seriallayout reconfigurable main-arm (RMA), which can assemble into all of the revolute-jointed kinematically simple main-arm configurations presented by Podhorodeski and Pittens. 6 Yang et al 7 discuss issues surrounding the kinematic design of three-legged modular parallel manipulators. They use an example modular parallel manipulator which is reconfigurable in branch structure.…”

“…The branch structures are based mainly on the kinematically simple branch structures of Podhorodeski 8 and Podhorodeski and Pittens. 6 Redundantly actuated parallel manipulators have also been designed. For example, Cheng et al 9 consider the dynamics and control of redundantly actuated parallel manipulators.…”