Non-singular assembly mode changing trajectories in the workspace for the 3-RPS parallel robot

Having non-singular assembly modes changing trajectories for the 3-RPS parallel robot is a well-known feature. The only known solution for defining such trajectory is to encircle a cusp point in the joint space. In this paper, the aspects and the characteristic surfaces are computed for each operation mode to define the uniqueness of the domains. Thus, we can easily see in the workspace that at least three assembly modes can be reached for each operation mode. To validate this property, the mathematical analysis of the determinant of the Jacobian is done. The image of these trajectories in the joint space is depicted with the curves associated with the cusp points

Parallel Manipulators with Lower Mobility

A review of the criteria to be used for designing parallel manipulators with lower mobility (LM-PMs) is presented. This chapter attempts to provide a unified frame for the study of this type of machines together with a critical analysis of the vast literature about them. The chapter starts with the classification of the LM-PMs, and, then, analyzes the specific subjects involved in the functional design of these machines. Special attention is paid to the definition of the limb topology, the singularity analysis and the discussion of the characteristics of some machines

Non-Singular Assembly Mode Changing Trajectories of a 6-DOF Parallel Robot

International audienceThis paper deals with the non-singular assembly mode changing of a six degrees of freedom parallel manipulator. The manipulator is composed of three identical limbs and one moving platform. Each limb is composed of three prismatic joints of directions orthogonal to each other and one spherical joint. The first two prismatic joints of each limb are actuated. The planes normal to the directions of the first two prismatic joints of each limb are orthogonal to each other. It appears that the parallel singularities of the manipulator depend only on the orientation of its moving platform. Moreover, the manipulator turns to have two aspects, namely, two maximal singularity free domains without any singular configuration, in its orientation workspace. As the manipulator can get up to eight solutions to its direct kinematic model, several assembly modes can be connected by non-singular trajectories. It is noteworthy that the images of those trajectories in the joint space of the manipulator encircle one or several cusp point(s). This property can be depicted in a three dimensional space because the singularities depend only on the orientation of the moving-platform and the mapping between the orientation parameters of the manipulator and three joint variables can be obtained with a simple change of variables. Finally, to the best of the authors' knowledge, this is the first spatial parallel manipulator for which non-singular assembly mode changing trajectories have been found and shown

A generalized approach for computing the transmission index of parallel mechanisms

This paper presents a novel approach for computing the transmission index of parallel mechanisms. The approach is based on an extended concept to compute the maximal virtual coefficient, which is an important notion involved in the formulation of dimensionally homogeneous transmission indices for singularity analysis and dimensional optimization of parallel mechanisms. By exploiting the dual property of the virtual coefficient, two characteristic points instead of one as in the current state of the art are defined: one characteristic point – termed the transmission characteristic point – is located on the ‘floating’ axis of the transmission wrench, as in existing approaches, while a second one – termed the output characteristic point – is located on the floating axis of the output twist of the platform, which is a novel concept. This allows one to define two characteristic lengths, namely, the transmission and output characteristic lengths, respectively, of which the larger is then used for the measure of the “distance” between the transmission wrench screw and the output twist screw. As shown in this paper, this new measure makes it possible to discern more finely the configuration-dependent properties of kinematic performance of parallel mechanisms, thus making it more suitable for dimensional optimization. Confidence in this statement is demonstrated through the comparative study of two in-parallel mechanisms using the new method and previously existing ones