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Image of two link manipulator

My professor described the end effector position as $q_{e} = \begin{bmatrix} x_e \\y_e\end{bmatrix} = \begin{bmatrix} l_1 cos(\alpha_1) + l_2cos(\alpha_1 + \alpha_2) \\ l_1 sin(\alpha_1) + l_2sin(\alpha_1 + \alpha_2) \end{bmatrix}$

Why isn't the expression $\begin{bmatrix} l_1 cos(\alpha_1) + l_2cos(\alpha_1 - \alpha_2) \\ l_1 sin(\alpha_1) + l_2sin(\alpha_1 - \alpha_2) \end{bmatrix}$

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  • $\begingroup$ Could $/alpha2$ be negative? Itself...as in $\alpha_1 + (-)\alpha_2$ ? But in reality, the total angle is additive. $\endgroup$ – morbo Sep 23 '19 at 19:51
  • $\begingroup$ @morbo I assumed the arrow associated with the angle was the direction of rotation but I was told that the total angle should be additive. $\endgroup$ – Drew Sep 23 '19 at 20:03
  • $\begingroup$ And the total angle is additive. $\endgroup$ – morbo Sep 23 '19 at 20:08

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