Inverse kinematics of 6-links manipulator

As promised in the previous article.

Let’s look at direct kinematics.
H = T_z(L_0) \cdot R_z(q_1) \cdot T_z(L_{11}) \cdot T_x(L_{12}) \cdot R_y(q_2) \cdot T_z(L_2) \cdot R_y(-q_3) \cdot T_z(L_{31}) \cdot R_x(-q_4) \cdot T_x(L_4) \cdot R_y(-q_5) \cdot T_x(L_5) \cdot R_x(-q_6)

Where T_a – translation matrix with respect to a axis, and R_a – rotational matrix with respect to a axis.
H – homogeneous transformation matrix, which contains the position and rotation of the endpoint in global coordinates. (L_{32} is already included in L_4 because there is no difference where J_4 is located on this link)

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Inverse kinematics of 2 and 3-links manipulator

With direct kinematics for an ordinary manipulator, everything is pretty simple. And what about the inverse? At a minimum, it’s worth to repeat that it is ambiguous. Let’s start with the two-links manipulator.

2-links manipulator
2-links manipulator
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