Serial6R.world File Reference

Detailed Description

[Introduction] [Geometry] [Process] [Statistics] [Results] [References]

Introduction

A 6R serial chain has 16 solutions, the maximum possible number of solutions such a chain can have. Some methods exists to solve this paticular problem in miliseconds [Manocha and Canny 1994], but we use this benchmark as a test of the generality of the methods in the CuikSuite.

Geometry

Denavit-Hartenberg parameters for these parameters are:

i $a_i$ $d_i$ $\alpha_i$ Interpretation
1 0.3 0.0106 $\pi/2$
2 1 0 0.0175
3 0 0.2 $\pi/2$
4 1.5 0 0.0175
5 0 0 $\pi/2$
6 1.1353 0.1049 1.4716

Process

This example is treated following these steps (from the main CuikSuite folder):

  • Generate the equations: Execute
  • Solve the positional analysis problem: Execute
  • Visualize the solutions:

Statistics

Characteristics of the problem:

Nr. of indep. loops 1
Nr. of links 6
Nr. of joints 6
Nr. of equations (in the simplified system) 20
Nr. of variables (in the simplified system) 19

Here you have the statistics about the execution (on an Intel Core i7 at 2.9 Ghz).

Nr. of Empty boxes 7
Nr. of Solution boxes 16
Execution time (s) 1

Results

Here you have the 16 solutions of this problem:

References

  • D. Manocha and J.F. Canny, "Efficient Inverse Kinematics for General 6R Manipulators", IEEE Transactions on Robotics and Automation, Vol. 10., Nr. 5, pp. 648-657, October 1994.
  • J. M. Porta, L. Ros and F. Thomas. "A linear relaxation technique for the position analysis of multiloop linkages". IEEE Transactions on Robotics, 25(2): 225-239, 2009.
  • M. Raghavan and B. Roth, "Inverse Kinematics of the general 6R manipulator and related linkages", ASME Journal of Mechanical Design, Vol. 115, pp. 502-508, 1993.
  • C. Wampler and A.P. Morgan, "Solving the 6R inverse position problem using a generic-case solution methodology", Mechanisms Mach. Theory, Vol. 26, Nr. 1, pp. 91-106, 1991.

Definition in file Serial6R.world.