3.3.1 A 2D Kinematic Chain

Before considering a kinematic chain, suppose ${\cal A}_1$ and ${\cal A}_2$ are unattached rigid bodies, each of which is capable of translating and rotating in ${\cal W}= {\mathbb{R}}^2$. Since each body has three degrees of freedom, there is a combined total of six degrees of freedom; the independent parameters are $x_1$, $y_1$, $\theta_1$, $x_2$, $y_2$, and $\theta_2$.