OPTIMAL SYNTHESIS OF PLANAR 4 LIMBS 3-DOF OVERACTUATED PARALLEL MECHANISMS

Optimal synthesis of a 3-DOF 4 limbs planar parallel mechanism with actuated redundancy is studied. The kinematics equation of the mechanism is developed and the topology of the mecha-nism is classified. The kinematics and force properties of the mechanisms according to the topologies are compared. Furthermore, a global optimizing formulation is derived from the condition number that is a local index usually used to scaling the manipulability isotropy quantitatively. The optimiza-tion is solved by genetic algorithm. The numerical results show that the topology of the mechanisms can influence the kinematics and force property considerably, and the manipulation dexterity of the mechanisms can be improved distinctly by the given formulations and the suggested optimization algorithm.     

On the Lagrangian and Cartesian Stiffness Matrices of Parallel Mechanisms with Elastic Joints

In this paper an analytical formulation is proposed of the Lagrangian and Cartesian stiffness matrices for parallel mechanisms with rigid bodies and elastic joints. The formulation is general, as it is based on the development of the principle of virtual work and on the definition of the stiffness matrices. A relationship is also obtained between the Lagrangian and Cartesian stiffness matrices. Each contribution to the stiffness matrices is explicitly expressed in order to gain insight into their physical meaning and mathematical nature. In the paper, three numerical examples are presented. Indeed, the stiffness matrices are calculated for three planar mechanisms. The computation method exploits the multiple closed-chain architecture in parallel architectures. For this reason, it can be performed without encountering practical difficulties.     

Computational study on planar dominating set problem

Recently, there has been significant theoretical progress towards fixed-parameter algorithms for the DOMINATING SET problem of planar graphs. It is known that the problem on a planar graph with n vertices and dominating number k can be solved in time using tree/branch-decomposition based algorithms. In this paper, we report computational results of Fomin and Thilikos algorithm which uses the branch-decomposition based approach. The computational results show that the algorithm can solve the DOMINATING SET problem of large planar graphs in a practical time and memory space for the class of graphs with small branchwidth. For the class of graphs with large branchwidth, the size of instances that can be solved by the algorithm in practice is limited to about one thousand edges due to a memory space bottleneck. The practical performances of the algorithm coincide with the theoretical analysis of the algorithm. The results of this paper suggest that the branch-decomposition based algorithms can be practical for some applications on planar graphs.     

Synthesis on forward kinematics problem algebraic modeling for the planar parallel manipulator: displacement-based equation systems

Based on a proven exact method which solves the forward kinematics problem (FKP) this article investigates the FKP formulation specifically applied to planar parallel manipulators. It focuses on the displacement-based equation systems. The majority of planar tripods can modeled by the 3-RPR parallel manipulator, which is a tripod constituted by a fixed base and a triangular mobile platform attached to three kinematics chains with linear (prismatic) actuators located between two revolute joints. In order to implement the algebraic method, the parallel manipulator kinematics are formulated as polynomial equation systems where the number of equations is equal to or exceeds the number of unknowns. Three geometrical formulations are derived to model the difficult FKP. The selected proven algebraic method uses Gröbner bases from which it constructs an equivalent univariate system. Then, the real roots are isolated using this last system. Each real solution exactly corresponds to one manipulator assembly mode, which is also called a manipulator posture. The FKP resolution of the planar 3-RPR parallel manipulator outputs six complex solutions which become a proven real solution number upper bound. In several typical examples, the resolution performances (computation times and memory usage) are given. It is then possible to compare the models and to reject one. Moreover, a number of real solutions are obtained and the corresponding postures drawn. The algebraic method is exact and produces certified results.     

Design of surface wave active beds based on human tissue physiology

A surface wave distributed actuation method and its proper design for safely transporting bedridden patients is explored in this paper. First, the basic principle of surface wave distributed actuation is presented, including a new kinematic feature that augments natural surface wave motion for enhanced transport efficiency of humans and elastic bodies. Kinematic modeling and analysis reveals that an object can be transferred by a simplified actuator architecture that makes the concept amenable to hardware realization. A proof of concept prototype demonstrates that heavily loaded rigid objects, elastic objects and humans can be transported. Human tissue physiology is studied to establish worst-case criteria for safe and healthy interactions between the human and the support surface that depends on the duration of interaction. Static models are developed and solved using finite element methods to calculate interaction stresses for realistic, worst-case human-surface wave interaction scenarios. Based on these results a new two-mode surface is designed to secure safe interactions for both long-term support and short term transport tasks.