Serial6R Directory Reference

Detailed Description

[Introduction] [Geometry] [Formulations] [References]

Introduction

A 6R manipulator is a chain of seven links L0,L1, ..., L6, where Li is connected to Li+1 with a revolute joint. Link L0 is the "ground" and link L6 is the "end effector" (usually a gripper). The problem is to compute which joint angles are required to place the end effector at a given position and orientation in 3-space. Note that, since the ground and the end effector have fixed relative positions, they can be viewed as a single rigid body. Thus, the inverse kinematic problem is equivalent to finding all possible configurations of a general 6R loop like the one depicted above.

For more than a decade this was one of the principal problems of Robot Kinematics. The first efficient solution is due to [Raghavan and Roth 1993] who obtained a minimum-degree resultant for this problem. Using this technique, the problem can be solved in a few milliseconds on a standard computer [Manocha and Canny 1994]. Although the CUIK solution is slower, it is less affected by the presence of equation singularities, and it can deal with paradoxical 6R loops with positive-dimensional solution spaces.

Geometry

The usual way to parametrize a serial chain is giving the Denavit-Hartenberg parameters. In this convention, three parameters ( $ a_i, d_i, \alpha_i $) relate the frame of reference attached to link $i$ with that attached to link $i+1$. See the figure below for an interpretation of these parameters.

Denavit-Hartenberg parameters relating link i and link i+1

Formulations

In this directory the following 6R-chain formulations are provided:

Please, check the individual files for the Denavit-Hartenberg in each case.

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, F. Thomas, "Multi-loop Position Analysis via Iterated Linear Programming", in Proc. Robotics: Science and Systems II, Philadelphia, USA, 2006.
  • E. J. F. Primrose, "On the input-output equation of the general 7R mechanism", Mechanisms and Machine Theory, Vol. 21, pp. 509-510, 1986.
  • 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.

Files

file  Serial6R.world [code]
 A general Serial6R mechanism.
 
file  Serial6R1dof.world [code]
 An architecturally singular Serial6R mechanism.
 
file  Serial6RBricard.world [code]
 A general Serial6R mechanism.
 
file  Serial6RRX60.world [code]
 An industrial Serial6R mechanism.