3R.world File Reference

Detailed Description

Determining the workspace boundaries of a 3R planar robot.

You can get an idea of the workspace to bound executing;

The point to track is the one in green. Each red dot is a revolute joint, where all rotation axis are parallel.

To process this problem you have to generate the equations executing either

or

  • bin/cuikTWS examples/WSSingularities/3R end_effector
  • bin/cuik examples/WSSingularities/3R_TWS
  • bin/cuikplot examples/WSSingularities/3R_TWS 9 10 workspace3R
  • xfig workspace3R.fig

The output is a set of one-dimensional curves that bound the translational workspace of the robot. In both cases the process takes about 3 minutes and generates about 4800 boxes

bin/cuiksimplify and bin/cuikaddjacobian are intended to be tools to define the equation set to analyze the singularities on any subset of variables. The workspace boundaries are singularities on the varariables giving the position of the end effector link. bin/cuikTWS is a tool specific to generate the equations characterizing translational workspaces.

In both cases the execution takes about 200 seconds and generate about 4800 solution boxes. In both cases you will get a planar plot of the translatinal workspace of the interest variables (the area reachable for the end effector, that is a particular point on the last link of the robot).

To obtain a 3D plot you can execute:

  • bin/cuikplot3d examples/WSSingularities/3R_sing_simp_J 9 11 10 0 workspace3R

or

  • bin/cuikplot3d examples/WSSingularities/3R_TWS 9 11 10 0 workspace3R

and then visualize the output

  • scripts/cuikmove examples/WSSingularities/3R
  • Load the file workspace3R.gcl using the geomview main menu (File->Open)
  • Set the camera to orthographic view (geomview menu Inspect->Cameras and then set the Orthographic option)
  • Look the full scene (Press button look) and rotate it until you view the image below (view the image orthogonal to the X-Z plane containing the robot).
  • Move the sliders to see how the end effector (the green dot) remains in the computed boundaries. The interesting situations occur when the sliders (one or more than one) are in the extreme of their ranges.

Definition in file 3R.world.