The optimum kinematic design of a spherical three-degree-of-freedom parallel manipulator
01 Mar 1988-Journal of Mechanisms Transmissions and Automation in Design (American Society of Mechanical Engineers)-Vol. 110, Iss: 1, pp 202-207
TL;DR: Optimisation de la cinematique d'un manipulateur utilisant un mecanisme parallele spherique a trois degres de liberte.
Abstract: Optimisation de la cinematique d'un manipulateur utilisant un mecanisme parallele spherique a trois degres de liberte
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01 Jun 1990
TL;DR: The different kinds of singularities encountered in closed-loop kinematics chains are analyzed and a general classification of these singularities in three main groups, based on the properties of the Jacobian matrices of the chain, is described.
Abstract: The different kinds of singularities encountered in closed-loop kinematics chains are analyzed. A general classification of these singularities in three main groups, which is based on the properties of the Jacobian matrices of the chain, is described. The identification of the singular configurations is particularly relevant for hard automation modules or robotic devices based on closed kinematic chains, such as linkages and parallel manipulators. Examples are given to illustrate the application of the method to these mechanical systems. >
1,648 citations
TL;DR: In this article, a performance index for the kinematic optimization of robotic manipulators is presented based on the condition number of the Jacobian matrix of the manipulator, which is known to be a measure of the amplification of the errors due to the joint and Cartesian spaces.
Abstract: In this paper, a novel performance index for the kinematic optimization of robotic manipulators is presented. The index is based on the condition number of the Jacobian matrix of the manipulator, which is known to be a measure of the amplification of the errors due to the kinematic and static transformations between the joint and Cartesian spaces. Moreover, the index proposed here, termed global conditioning index (CGI), is meant to assess the distribution of the aforementioned condition number over the whole workspace. Furthermore, the concept of a global index is applicable to other local kinematic or dynamic indices. The index introduced here is applied to a simple serial two-link manipulator, to a spherical three-degree-of-freedom serial wrist, and to three-degree-of-freedom parallel planar and spherical manipulators. Results of the optimization of these manipulators, based on the GCI, are included.
884 citations
TL;DR: A review of the literature on the six-degree-of-freedom parallel manipulator commonly known as the Stewart platform can be found in this article, where the authors highlight the distinctions of this class from the conventional serial robot manipulators and the novel perspectives that are necessary for the analysis and design of the Stewart platforms in particular and parallel manipulators in general.
637 citations
01 Jun 1990
TL;DR: The approach used by the author is to establish stiffness or conditioning maps of the workspace of the manipulator, which reveal the existence of zones where the stiffness is not acceptable and also help the designer by providing a more accurate representation of the properties of the manipulation.
Abstract: Mechanical systems containing closed-loop kinematic chains can exhibit special types of singularities that result in a loss of controllability of the element of interest (output link or gripper link). Therefore, it is very important for the designer to be able to predict this type of behavior. The approach used by the author is to establish stiffness or conditioning maps of the workspace of the manipulator. A method for obtaining these maps for planar and spatial parallel manipulators is presented. The maps reveal the existence of zones where the stiffness is not acceptable and also help the designer by providing a more accurate representation of the properties of the manipulator. >
515 citations
TL;DR: In this paper, the Kutzbach-Grubler mobility criterion is used to calculate the degrees of freedom of a general mechanism, but the criterion can break down for mechanisms with special geometries, and in particular, the class of overconstrained parallel mechanisms.
Abstract: The Kutzbach-Grubler mobility criterion calculates the degrees of freedom of a general mechanism. However, the criterion can break down for mechanisms with special geometries, and in particular, the class of so-called overconstrained parallel mechanisms. The problem is that the criterion treats all constraints as active, even redundant constraints, which do not affect the mechanism degrees of freedom. In this paper we reveal a number of screw systems of a parallel mechanism, explore their inter-relationship and develop an original theoretical framework to relate these screw systems to motion and constraints of a parallel mechanism to identify the platform constraints, mechanism constraints and redundant constraints. The screw system characteristics and relationships are investigated for physical properties and a new approach to mobility analysis is proposed based on decompositions of motion and constraint screw systems. New versions of the mobility criterion are thus presented to eliminate the redundant constraints and accurately predict the platform degrees of freedom. Several examples of overconstrained mechanisms from the literature illustrate the results.
372 citations