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Old Dec 14th 2017, 12:34 AM   #1
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Forward and Inverse Kinematics

Imagine that you have a robot that is similar to a wrist with its first two axes. Then, at the end of the second link, you have a translational third link that is orthogonal to the plane that the second link is on. That is, if the zero position for the first two links is in the X-Z plane, the rotations of the first two links are around the Z and Y planes respectively, and the translation of the third link happens in the Y-direction.
--Work out the forward and inverse position kinematics for this robot. Assume that you can
use known values L1 and L2 for the first two links. Keep in mind that L3 now is a variable
that you need to solve for, just like the first two angles. (Assume that in the zero position,
you are at the coordinate [0 L3, L1+L2)

Is anyone able to show me show to set this up in matrix form?
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Old Dec 14th 2017, 09:59 AM   #2
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I was thinking Qf should be Q1tau1+Q1Q2tau2+Q1Q2tau3

My logic was that because the third link is translational so Q3 would not exist in the equation...not sure if i am on the right track.
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Old Dec 15th 2017, 06:39 PM   #3
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I'm not sure but...

My thinking would be to take it in stages.

I would take the third link first:
=[Q3].L3

next we add in the second link and apply the second rotation:
=[Q2].{([Q3].L3)+L2}

Now we add in the first link and apply the first rotation
=[Q1].([Q2].{([Q3].L3)+L2}+L1)

Watch out for all the brackets...

Note that since matrix multiplication is distributive this can be expanded:
=[Q1].[Q2].[Q3].L3+[Q1.][Q2].L2+[Q1].L1
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Last edited by Woody; Dec 15th 2017 at 06:45 PM.
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