Question

1. Given 「R11 R12 R13 Px1 ST-l R21 R22 R23 P, 3 - R31 R32 R33 Pz 0 001 Find θ1, θ2, θ3 of the 3R nonplanar manipulator. You can use the forward kinematics solution from previous homework directly L.2 02

Answer 1

The solution for a 3 dof transformation matrix can be seen as

cos(9 Cos(9 +9 ) -cos(9 ) sin( θ +8 ) -sin(θ)sin(0,+9) sin( θ ) -cos(θ) ( .4 + B cos( θ ))cos(9 ) (.4 + Bcos(θ))sin(θ) sin( θ )cos(θ+8, ) sin(0,+0,) "I' (TXT ) Sin

A= L₁

B = L₂

clearly R₁₃/R₂₃ = -tan(θ₁)

θ₁ = -tan^-1(R₁₃/R₂₃)

Also R₃₁/R₃₂ = tan(θ2+θ3)

θ₂+θ₃ = tan-1(R₃₁/R₃₂)

Also

L₂sin(θ2) = P_z

θ2= sin^-1(P_z/L₂)

Hence θ_{3 =} tan-1(R₃₁/R₃₂) - sin^-1(P_z/L₂)

Please upvote if this answer was helpful! Also do mention any doubts in the comments!! :)