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Let's consider four points $A, B, C$ and $D$ and let us consider the parameter $d$, as shown in the figures below. And let us consider $p_e=\begin{Bmatrix}0\\0\\0\\1\end{Bmatrix}$ to be the end-effector location in end-effector's coordinate system. Now, there are two ways of connecting the origin and the end-effector position, namely $O-A-P$ and $O-C-B-P$. ...

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I've found the solution. Instead of using intrinsic matrix to angle conversions such as: $yaw = atan2(R_{n_{1}\leftarrow n_{2}}(2,1),R_{n_{1}\leftarrow n_{2}}(1,1))$ $pitch = asin(−R_{n_{1}\leftarrow n_{2}}(3,1))$ $roll = atan2(R_{n_{1}\leftarrow n_{2}}(3,2),R_{n_{1}\leftarrow n_{2}}(3,3))$ I should use extrinsic matrix to angle conversions such as: \$yaw = ...

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Looks like a 4-bar slider-crank system with a linear output. Generally, with these closed-chain kinematics, you need to compute the end-effector pose (point P) from two open chains with one open chain starting at link 1 to link 2 and the other open chain starting at link 3 to link 2. Then you need to solve for the generalized coordinates, which from your ...

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