Institut de Robòtica i Informàtica Industrial
KRD Group

The CuikSuite Project

Serial6RBricard.world File Reference

A general Serial6R mechanism. More...

Go to the source code of this file.

Detailed Description

bricard.jpg

Introduction

A closed kinematic chain consisting of six binary links, connected together by six revolutes is generally rigid, i.e., it can only be assembled in a finite number of different ways. However, if there are certain geometrical conditions imposed upon the relevant linkage parameters (the normal distances, the twist angles and the offsets of the revolutes on each of the links) the chain my be mobile with one degree of freedom. Such 6R loops are said to be overconstrained mechanisms, and one example is "rectangular Bricard chain" shown above [Wohlhart 1987].

The Bricard chain belongs to a larger family of overconstrained 6R loops, characterized by the fact that in every position of the linkage there is a transversal, a straight line that intersects all six revolute axes-lines. In the case of the rectangular Bricard chain, if we number the revolute axis lines from 1 to 6 consecutively, the even numbered ones and the odd numbered ones meet in all positions at points $P_{135}$ and $P_{246}$, respectively [Wohlhart 1987], and the transversal is the line defined by these two points (see the figure above).

The Denavit-Hartenberg parameters of the Bricard 6R loop are:

i $a_i$ $d_i$

$\alpha_i$

1

1 0 $\pi/2$

1

1 0 $\pi/2$

1

1 0 $\pi/2$

1

1 0 $\pi/2$

1

1 0

$\pi/2$

Resolution

See DoubleButterfly for an extensive step-by-step explanation of how to perform position analysis and path planning within the CuikSuite. Next, we briefly enumerate those steps:

  • Generate the equations: Execute
  • Solve the positional analysis problem: Execute
    • cuik examples/Serial6R/Serial6RBricard_kin
  • Examine the solutions:
    • Inspect the resulting solution file (Serial6RBricard_kin.sol) with the original set of equations, the simplified set, the set of solutions and the statistics on the solving proces.
    • Generate 3d projections of the solution points with cuikplot3d.
    • Generate snapshots of the valid poses of the 6R chain using cuikanimate. For this it is better to store one solution at a time in a temporal sol file. In this case the animation produces a still image (otherwise the animation jumps between the valid, disconnected configurations).

References

  • K. Wohlhart, "A New 6R Space Mechanism", 7th World Congress on the Theory of Machines and Mechanisms. Vol. 1, pp. 193-198, Sevilla, Spain, 1987.

Definition in file Serial6RBricard.world.