An Interval Analysis Based Study for the Design and the Comparison of Three-Degrees-of-Freedom Parallel Kinematic Machines

Abstract

This paper addresses an interval analysis based study that is applied to the design and the comparison of 3-DOF parallel kinematic machines. Two design criteria are used, (i) a regular workspace shape and, (ii) a kinetostatic performance index that needs to be as homogeneous as possible throughout the workspace. The interval analysis based method takes these two criteria into account: on the basis of prescribed kinetostatic performances, the workspace is analysed to find out the largest regular dextrous workspace enclosed in the Cartesian workspace.An algorithm describing this method is introduced. Two 3-DOF translational parallel mechanisms designed for machining applications are compared using this method. The first machine features three fixed linear joints which are mounted orthogonally and the second one features three linear joints which are mounted in parallel.In both cases, the mobile platform moves in the Cartesian x − y − z space with fixed orientation.

Interval Analysis and Robotics

“…Natural evaluation may be simply illustrated with f = x 2 − 2x when x lie in the range [3,5]. In that case we can safely state that for any instance of x in [3,5], then x 2 lie in [9,25], 2x in [6,10] and consequently −2x in [-10,-6].…”

“…Natural evaluation may be simply illustrated with f = x 2 − 2x when x lie in the range [3,5]. In that case we can safely state that for any instance of x in [3,5], then x 2 lie in [9,25], 2x in [6,10] and consequently −2x in [-10,-6]. Summing the interval for x 2 and −2x leads to [9,25]+[-10,-6]= [-1,19] which constitutes the interval evaluation of f over the range [3,5].…”

“…In that case we can safely state that for any instance of x in [3,5], then x 2 lie in [9,25], 2x in [6,10] and consequently −2x in [-10,-6]. Summing the interval for x 2 and −2x leads to [9,25]+[-10,-6]= [-1,19] which constitutes the interval evaluation of f over the range [3,5]. Interval evaluation may also be obtained using other methods (Taylor expansion, centered form) and is sensitive to the analytical form used for the function.…”

Dynamic Model of a 6-dof Parallel Manipulator Using the Generalized Momentum Approach

“…Parallel manipulators are well known because of their high dynamic performances and low positioning errors (Chablat et al, 2004;Merlet, 2006). In the last few years parallel manipulators have attracted great attention from researchers involved with robot manipulators (Bruzzone, 2005), robotic end effectors (Vischer & Clavel, 2000), robotic devices for high-precision robotic tasks (Pernette, et al, 2000), machine-tools (Zhang & Gosselin, 2002), simulators (Kim et al, 2002), and haptic devices (Constantinescu et al, 2005).…”

Kinematic Performances of a Novel TLPM Parallel Robot

“…Much research has been devoted to the study of mechanical these criterias of a parallel mechanism [10,11,12]. Firmani and Podhorodeski [13] described singularity of planar parallel manipulators based on forward kinematic solutions.…”