Solved in this paper is the inverse kinematic problem asso ciated with manipulators of arbitrary architecture. Its formu lation is based on invariants in the rotational part of the closure equations, which produces a formally overdetermined nonlinear algebraic system. In the translational part, a recur sive scheme similar to that of Horner's for polynomial evalu ation is introduced. This leads to a reduced number of com putations, which allows an efficient numerical solution of the problem. Velocity and acceleration kinematic inversions are also included. The procedure is illustrated with the analysis of a six-degree-of-freedom, revolute-coupled manipulator of an architecture that makes a closed-form solution difficult. This method has been successfully applied to the analysis of 7R spatial linkages as well. Appendix A lists the nomenclature and notation used in this paper.

On the Numerical Solution of the Inverse Kinematic Problem

Defects in link mechanisms and solution rectification

We study the path planning problem, without obstacles, for closed kinematic chains with n links connected by spherical joints in space or revolute joints in the plane. The configuration space of such systems is a real algebraic variety whose structure is fully determined using techniques from algebraic geometry and differential topology. This structure is then exploited to design a complete path planning algorithm that produces a sequence of compliant moves, each of which monotonically increases the number of links in their goal configurations. The average running time of this algorithm is proportional to n3. While less efficient than the O(n) algorithm of Lenhart and Whitesides, our algorithm produces paths that are considerably smoother. More importantly, our analysis serves as a demonstration of how to apply advanced mathematical techniques to path planning problems.Theoretically, our results can be extended to produce collision-free paths, paths avoiding both link—obstacle and link—link collisions. An...

Complete Path Planning for Closed Kinematic Chains with Spherical Joints

https://openaccess.iyte.edu.tr/bitstream/11147/4743/1/4743.pdf

Structural synthesis of parallel manipulators

A robot essentially acts by moving in a physical world. The motion planning capability is thus a fundamental issue for the autonomy of the system, and represents a very active area of research in Robotics. Furthermore, the interest in motion planning techniques goes beyond robotic applications. Currently, these techniques are applied in other very different domains such as : CAD/CAM, industrial logistics, graphic animation, or computational Biology. Complex articulated mechanisms containing closed kinematic chains appear in all these domains. This thesis treats motion planning for such systems. The first part contains our theoretical and technical work. We introduce samplingbased planners into a general formulation of the motion planning problem in presence of kinematic closure constraints. The algorithmic tools that we propose allow an efficient application of these techniques to complex closed-chain mechanisms. The second part deals with the different fields of application that we have investigated. In Robotics, our approach has been applied to motion synthesis of parallel robots, coordinated manipulation and manipulation planning. Finally, we discuss an original application to Structural Biology for the conformational analysis of protein loops. The results of our experiments prove the efficacy and the generality of the approach.

/pdf/motion-planning-algorithms-for-general-closed-chain-36gks9bgza.pdf

Rasim I Alizade

Papers

Determination of the condition of existence of complete crank rotation and of the instantaneous efficiency of spatial four-bar mechanisms

Type synthesis of spatial mechanisms on the basis of spatial single loop structural groups

Mathematical models for analysis and synthesis of spatial mechanisms—II

Mathematical models for analysis and synthesis of spatial mechanisms—III Six-link spatial mechanisms