Jean-François Collard

Simplified static analysis of large-dimension parallel cable-driven robots

This paper introduces a new simplified static analysis of parallel robots driven by inextensible cables of non-negligible mass. It is based on a known hefty cable static modeling which seems to have been overlooked in previous works on parallel cable-driven robots. This cable modeling is obtained from a well-known sagging cable modeling, known as the catenary, by assuming that cable sag is relatively small. The use of the catenary has been shown to lead to a non-linear set of equations describing the kinetostatic behavior of parallel robots driven by cables of non-negligible mass. On the contrary, the proposed simplified static analysis yields a linear relationship between (components of) the forces in the cables and the external wrench applied to the robot mobile platform. As a consequence, by means of the simplified static analysis, useful wrench-based analysis and design techniques devised for parallel robots driven by massless cables can now be extended to cases in which cable mass is to be accounted for.

Geometry Selection of a Redundantly Actuated Cable-Suspended Parallel Robot

This paper is dedicated to the geometry selection of a redundantly actuated cable-suspended parallel robot intended to manipulate heavy payloads over a wide workspace. Cable-suspended refers here to cable-driven parallel robots in a crane-like setting, where all the cable drawing points are located on top of the base frame, gravity being used to keep the cables taut. Geometry selection consists of determining the relative positions of the cable drawing points on the base frame and of the cable attachment points on the mobile platform together with the cable arrangement between these two sets of points. An original performance index is introduced. It is defined as the maximum acceptable distance between the mobile platform geometric center and the center of mass of the set consisting of the platform and a payload. This performance index is of particular interest in heavy payload handling applications. Used within a two-phase geometry selection strategy, it yields a new cable-suspended robot geometry having a very large workspace to footprint ratio and able to handle heavy payloads. A large-dimension redundantly actuated cable-suspended robot was built in order to demonstrate these capabilities.

Multi-Objective Optimization of Parallel Manipulators

This paper deals with the optimal dimensional design of Delta robot. The aim is to obtain a manipulator with maximum dexterity and minimum projected area of the occupied volume on the base plane. Two different optimization strategies, which cope with assembly difficulties, have been applied to solve this problem. Comparing optimized Delta robot with and without area reduction, results show an important reduction of area maintaining an acceptable dexterity.

Kinematical Optimization of Closed-Loop Multibody Systems

Applying optimization techniques in the field of multibody systems (MBS) has become more and more attractive particularly thanks to the increasing development of computer resources. One of the main issues in the optimization of MBS concerns closed-loop systems which involve non-linear assembly constraints that must be solved before any analysis. The question that is addressed is: how to optimize such closed-loop topologies when the objective function evaluation relies on the assembly of the system? The authors have previously proposed to artificially penalize the objective function when those assembly constraints cannot be exactly satisfied. However, the method has some limitations. The algorithm is based on some tuning parameters that may affect the optimization results. Moreover, the penalization is not smooth, making the use of gradient-based optimization algorithms difficult. The key idea of this paper, to improve the penalty approach, is to solve the assembly constraints as well as possible and use the residue of these constraints as a penalty term instead of an artificial value. The method is easier to tune since the only parameter to choose is the weight of the penalty term. Besides, the objective function is continuous throughout the design space, which enables the use of efficient gradient-based optimization methods such as the sequential quadratic programming (SQP) method. To illustrate the reliability and generality of the method, two applications are presented. They are related to kinetostatic performance of parallel manipulators. The first optimization problem concerns a 3-dof Delta robot with 5 design parameters and the second one deals with a more complex 6-dof model of the Hunt platform with 10 design variables.