Direct kinematics    Singularities   

Direct kinematics

Code: EJCK-DKPM-01

Find the poses of the platform of a Gough platform with the following locations of the attachment points.

on the base (x,y,z coordinates in the reference frame)

1. : -9.758000 9.098000 0
2. : 9.758000 9.098000 0
3. : 12.758000 3.902000 0
4. : 3.000000 -13.000000 0
5. : -3.000000 -13.000000 0
6. : -12.758000 3.902000 0

on the platform (x,y,z coordinates in the local frame)

1. : -3.000000 7.300000 0
2. : 3.000000 7.300000 0
3. : 7.821800 -1.052000 0
4. : 4.821800 -6.248000 0
5. :-4.821800 -6.248000 0
6. : -7.821800 -1.052000 0

The 6 leg lengths are:

1. : 51.746348
2. : 51.746348
3. : 50.304231
4. : 49.425510
5. : 49.425510
6. : 50.304231

• x,y,z coordinates of the center: 0,0, 50
• tilt of the platform around the x axis: 10 degrees

Answers

• provided by J-P. Merlet (February 2002)
  1. C programm compiled with gcc, freely available, see here
  2. 16 solutions
  3. computed in 570 ms (SunBlade 100), 310 ms (PC, Pentium III)

Code: EJCK-SPM-01

Being given the geometry of a Gough platform of bench EJCK-DKPM-01 determine if there is any singularity for this robot in the workspace defined by x,y in [-7,7], z in [45,50] and teta_x, teta_y, teta_z in [-10,10] degrees

Answers

• provided by J-P. Merlet (February 2002)
  1. C++ and Maple programm
  2. No singularity, verification in 1mn 22s (SunBlade 100), 46.56s (PC, Pentium III).
  3. Note 1: the algorithm use Maple for a pre-processing that has to be done only once for a given robot: if the pre-processing has been done beforehand the verification time is 8s (SunBlade), 3.25s (PC)
  4. Note 2: the computation may be done on a parallel computer
  5. The algorith is described in: Merlet J-P. et Daney D.
     A formal-numerical approach to determine the presence of singularity within the workspace of a parallel robot.
     In F.C. Park C.C. Iurascu, editor, Computational Kinematics, pages 167-176. Seoul, 20-22 Mai 2001

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