# Two Link Manipulator End Effector Position

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 $$\begin{bmatrix} l_1 cos(\alpha_1) + l_2cos(\alpha_1 - \alpha_2) \\ l_1 sin(\alpha_1) + l_2sin(\alpha_1 - \alpha_2) \end{bmatrix}$$

• Could $/alpha2$ be negative? Itself...as in $\alpha_1 + (-)\alpha_2$ ? But in reality, the total angle is additive. Sep 23 '19 at 19:51
• @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.
– Drew
Sep 23 '19 at 20:03
• And the total angle is additive. Sep 23 '19 at 20:08