Originally Posted by

**sklnner** Question: how do we solve SYSTEM 2 (see bellow) to prove SYSTEM 3?

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hello,

im having a little trouble with robotics, inverse kinematics and its equations

if you do have heard of robotics IK, then this should be fairly easy

its the simplest occasion (planar 2-link/2-dof/2r manipulator) from the introduction to kinematics (robotics)

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[L1, L2] = length of each link, [1, 2] = angles, [cos12] = cos(1 + 2), [sin12] = sin(1+2)

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SYSTEM 1 (forward kinematics equations)

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px = L1cos1 + L2cos12

py = L1sin1 + L2sin12

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SYSTEM 2 (rearrangement of system 1)

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px = (L1 + L2cos2)cos1 + (-L2sin2)sin1

py = (L2sin2)cos1 + (L1 + L2cos2)sin1

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SYSTEM 3 (system 2 solved for sin1, cos1)

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sin1 = px (-L2sin2) + py (L1 + L2cos2)

cos1 = px (L1 + L2cos2) + py (L2sin2)

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Question: How do we get from SYSTEM 2 to SYSTEM 3?

of course i dont expect an analytical answer, i wont bother you that much

i just hope for some internet directions since i dont know the correct english terms to run a proper search

the problem is that i have found different answers/ solutions for sin1, cos1 in different books but not one has the proof

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thank you