TABLE 2.

Parameters of the example constraints of Figure 2.

Figure 2 label	Constraint name	Constraint frame
		DOF	Type	Geometry
		${\mathit{d}}^{\varphi }$	$\left\{\varphi \right\}$	${\mathit{R}}^{\varphi }$	$-$
		${\mathit{d}}^{\psi }$	$\left\{\psi \right\}$	${\mathit{R}}^{\mathit{\psi }}$	${\mathit{p}}^{\psi }$
A	Revolute joint	$\left[0,1,0\right]$	$-$	$\left[-,{\mathit{r}}_y,-\right]$	$-$
		$\left[0,0,0\right]$	$-$	$\left[-,-,-\right]$	$\left[p_x,-,p_z\right]$
B	Prismatic joint	$\left[0,0,0\right]$	$-$	$\left[-,-,-\right]$	$-$
		$\left[1,0,0\right]$	$-$	$\left[{\mathit{r}}_x,-,-\right]$	$\left[-,-,-\right]$
C	Cylinder joint	$\left[1,0,0\right]$	$-$	$\left[{\mathit{r}}_x,-,-\right]$	$-$
		$\left[1,0,0\right]$	$-$	$\left[{\mathit{r}}_x,-,-\right]$	$\left[-,p_y,p_z\right]$
D	Plane-plane contact	$\left[0,0,1\right]$	$-$	$\left[-,-,{\mathit{r}}_z\right]$	$-$
		$\left[1,1,0\right]$	$-$	$\left[-,-,{\mathit{r}}_z\right]$	$\left[-,-,-\right]$
E	Planar contour following	$\left[0,1,0\right]$	$-$	$\left[-,{\mathit{r}}_y,-\right]$	$-$
		$\left[1,0,0\right]$	$\left\{\mathcal{B}\mathcal{B}\right\}$	$\left[{\mathit{r}}_x,-,-\right]$	$\left[p_x,-,-\right]$
F	Planar contour rolling	$\left[0,1,0\right]$	$-$	$\left[-,{\mathit{r}}_y,-\right]$	$-$
		$\left[1,0,0\right]$	$\left\{\mathcal{G}\mathcal{G}\right\}$	$\left[{\mathit{r}}_x,-,-\right]$	$\left[p_x,-,-\right]$
G	Cart on a curved surface	$\left[1,1,1\right]$	$-$	$\left[-,-,-\right]$	$-$
		$\left[1,1,0\right]$	$\left\{\mathcal{B}\mathcal{B}\right\}$	$\left[-,-,{\mathit{r}}_z\right]$	$\left[p_x,p_y,p_z\right]$
H	Contour rolling	$\left[1,1,1\right]$	$-$	$\left[-,-,-\right]$	$-$
		$\left[1,0,0\right]$	$\left\{\mathcal{G}\mathcal{G}\right\}$	$\left[{\mathit{r}}_x,-,-\right]$	$\left[p_x,p_y,p_z\right]$
I	Planar pin-plane contact	$\left[0,1,0\right]$	$-$	$\left[-,{\mathit{r}}_y,-\right]$	$-$
		$\left[1,0,0\right]$	$\left\{\mathcal{G}\mathcal{B}\right\}$	$\left[{\mathit{r}}_x,-,-\right]$	$\left[p_x,-,p_z\right]$
J	Planar plane-pin contact	$\left[0,1,0\right]$	$-$	$\left[-,{\mathit{r}}_y,-\right]$	$-$
		$\left[1,0,0\right]$	$\left\{\mathcal{B}\mathcal{G}\right\}$	$\left[{\mathit{r}}_x,-,-\right]$	$\left[p_x,-,p_z\right]$
K	Pin-plane contact	$\left[1,1,1\right]$	$-$	$\left[-,-,-\right]$	$-$
		$\left[1,1,0\right]$	$\left\{\mathcal{G}\mathcal{B}\right\}$	$\left[-,-,{\mathit{r}}_z\right]$	$\left[p_x,p_y,p_z\right]$
L	Plane-pin contact	$\left[1,1,1\right]$	$-$	$\left[-,-,-\right]$	$-$
		$\left[1,1,0\right]$	$\left\{\mathcal{B}\mathcal{G}\right\}$	$\left[-,-,{\mathit{r}}_z\right]$	$\left[p_x,p_y,p_z\right]$

“ $-$ ” means that entry is not uniquely defined.