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Description

The connection does not impose kinematic constraints. It defines three local directions ${e_{1}, e_{2}, e_{3}}$ as a function of the directions at both nodes a and b. These directions are not orthogonal and are identical to the successive rotation axes from a CARDAN connection. If $α$ is the first of the three Cardan angles that rotate the system at node a onto the system at node b,

e_{1} = e_{1}^{a}; e_{2} = \cos α e_{2}^{a} + \sin α e_{3}^{a}; and e_{3} = e_{3}^{b} .

The connection measures the change in position of node b relative to node a along the three non-orthogonal coordinate directions. Accordingly,

x = e^{1} \cdot (x_{b} - x_{a}); y = e^{2} \cdot (x_{b} - x_{a}); and z = e^{3} \cdot (x_{b} - x_{a}),

where ${e^{1}, e^{2}, e^{3}}$ are the dual basis directions defined by

e^{i} \cdot e_{j} = δ_{j}^{i}, where δ_{j}^{i} = 0 if i \neq j and δ_{j}^{i} = 1 if i = j .

The available components of relative motion are

u_{1} = x - x_{0}; u_{2} = y - y_{0}; and u_{3} = z - z_{0};

$x_{0}$ , $y_{0}$ , and $z_{0}$ are the initial coordinates of node b relative to node a along the initial ${e_{1}, e_{2}, e_{3}}$ directions. The connector constitutive displacements are

u_{1}^{m a t} = x - l_{1}^{r e f}; u_{2}^{m a t} = y - l_{2}^{r e f}; and u_{3}^{m a t} = z - l_{3}^{r e f} .

The kinetic force is

f_{p r o j C a r t} = f_{1} e^{1} + f_{2} e^{2} + f_{3} e^{3} .

In two-dimensional analysis $z = 0$ , $u_{3} = 0$ , $u_{3}^{m a t} = 0$ , and $f_{3} = 0$ .

Summary


PRISMATIC
Basic, assembled, or complex:	Basic
Kinematic constraints:	None
Constraint force output:	None
Available components:	$u_{1}, u_{2}, u_{3}$
Kinetic force output:	$f_{1}, f_{2}, f_{3}$
Orientation at a:	Optional
Orientation at b:	Optional
Connector stops:	$l_{1}^{m i n} \leq x \leq l_{1}^{m a x},$
	$l_{2}^{m i n} \leq y \leq l_{2}^{m a x},$
	$l_{3}^{m i n} \leq z \leq l_{3}^{m a x}$
Constitutive reference lengths:	$l_{1}^{r e f}, l_{2}^{r e f}, l_{3}^{r e f}$
Predefined friction parameters:	None
Contact force for predefined friction:	None