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nameFigure 1 2020-05-07 20-33-12.mp4
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Figure 1: Motion of the Main Mechanism

We can consider the mechanism to be divided into two parts:

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The height and offset of the top slot remains constant so we can find the length of d1 with simple trigonometry. 

Latex formatting
\begin{equation}
d_x{1x} = g - b_2\cos\theta_{32}
\end{equation}


\begin{equation}
d_y{1y} = f - b_2\sin\theta_{32}
\end{equation}


\begin{equation}
d_1 = \sqrt{d_{x}^2 + d_{y}^2}
\end{equation}