[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 | | | | Interpretation |
1 | 0.3 | 0.0106 | |
|
2 | 1 | 0 | 0.0175 |
3 | 0 | 0.2 | |
4 | 1.5 | 0 | 0.0175 |
5 | 0 | 0 | |
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.
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