Gripper

Event-driven compliant connection between two frames.

Description

The equations for the Gripper component are given below.

Reaction Forces:

where

 $\mathbf{F}$is the reaction force vector, $\mathbf{r}={\mathbf{r}}_{b}\mathbf{-}{\mathbf{r}}_{a}=⟨\left({x}_{b}-{x}_{a}\right),\left({y}_{b}-{y}_{a}\right),\left({z}_{b}-{z}_{a}\right)⟩$, is the relative displacement vector, ${\mathbit{r}}_{0}$, is the undeformed distance to frame_b from frame_a expressed along the inboard frame (frame_a), and $\mathbf{v}=\frac{d}{\mathrm{dt}}\mathbit{r},$is the relative velocity vector.

Reaction Torques:

Reaction torques are applied only when

where

 is the reaction torque vector, $\mathbf{\theta }$are the Euler angles - defined by the Rotation Sequence [1,2,3] and calculated from the relative rotation matrix of frame_b with respect to frame_a (see Euler Angle Sensor), ${\mathbf{\theta }}_{0}$, designates the undeformed rotation of frame_b with respect to frame_a, and $\mathbf{\omega }$$=⟨{\mathrm{ω}}_{x},{\mathrm{ω}}_{y},{\mathrm{ω}}_{z}⟩,$is the relative angular velocity vector.

Activation:

The actual reaction forces and torques applied depend on the values of $\mathrm{active}$ (Boolean Signal Input, see below), , and  (Boolean Parameter, see below). See the section Modes of Operation, below, for details. The reaction forces and torques are turned on and off according to the parameter $\mathrm{T__on/off}$ and the value of $\mathrm{active}$. This is controlled internally by an integer variable $\mathrm{state}$ described below.

 State Value Description 1 ON state. The state of the Gripper when $\mathrm{active}\mathbf{=}\mathbf{true}$ at initialization or $\mathrm{T__on/off}$ seconds have passed since $\mathrm{active}$ became true during simulation. In this state the reaction forces and torques are applied as described above. 2 ON2OFF state. The state of the Gripper when less than $\mathrm{T__on/off}$ seconds have passed since $\mathrm{active}$ became false during simulation. In this state the reaction forces and torques are multiplied by an internal variable $\mathrm{onoff}$ that decreases linearly from 1 to 0 over $\mathrm{T__on/off}$ seconds. Changing the value of $\mathrm{active}$ while in this state has no effect. 3 OFF state. The state of the Gripper when $\mathrm{active}\mathbf{=}\mathbf{false}$ at initialization or $\mathrm{T__on/off}$ seconds have passed since $\mathrm{active}$ became false during simulation. In this state there are no reaction forces and torques applied. 4 OFF2ON state. The state of the Gripper when less than $\mathrm{T__on/off}$ seconds have passed since $\mathrm{active}$ became true during simulation. In this state the reaction forces and torques are multiplied by an internal variable $\mathrm{onoff}$ that increases linearly from 0 to 1 over $\mathrm{T__on/off}$ seconds. Changing the value of $\mathrm{active}$ while in this state has no effect.

Note: If then the ON2OFF and OFF2ON states are never activated and $\mathrm{state}$ will only switch between the ON and OFF states.

Connections

 Name Description Modelica ID ${\mathrm{frame}}_{a}$ Inboard frame frame_a ${\mathrm{frame}}_{b}$ Outboard frame frame_b $\mathrm{active}$ Boolean signal to activate/deactivate the joint active

Modes of Operation

The Gripper has a number of settings that control the conditions under which the reaction forces and torques are applied:

 Case Use Torque Reactions In Place Description 1 The Gripper is activated and deactivated by an input boolean signal and only force reactions (due to translational springs) are applied. 2 Unlike case #1, the initial translational offset between frame_a and frame_b is used as the undeformed lengths of the translational springs. These undeformed lengths are updated any time the Gripper is not active and is then made active. 3 The same as case #1 and torque reactions (due to angular springs) are applied. When these options are selected the joint rotational stiffness and damping must be specified. 4 The same as case #2 and torque reactions (due to angular springs) are applied. When these options are selected the joint rotational stiffness and damping must be specified. The initial rotational offset between frame_a and frame_b is used as the undeformed angles of the angular springs. The undeformed angles are updated any time the Gripper is not active and is then made active.

Parameters

Symbol

Default

Units

Description

Modelica ID

$\mathrm{T__on/off}$

0.1

[s]

Time constant for activation/deactivation

T

All

-

With this enumeration, the directions in which the gripper applies reaction forces is controlled. There are seven choices:

 • All: Reactions are applied in X, Y, and Z axes (w.r.t. frame_a)
 • X and Y
 • Y and Z
 • Z and X
 • Only X
 • Only Y
 • Only Z

TransDir

$\mathrm{K__s}$

1e6

[N m]

Linear stiffness in all three directions.

cT

$\mathrm{K__d}$

1e3

[N s/m]

Linear damping coefficient in all three directions.

dT

-

When checked (true) torque reactions are also included.

useMoment

$\mathrm{K__θ}$

1e4

Angular stiffness for all three rotations ([1,2,3] Euler angles).

cR

$\mathrm{K__ω}$

1e2

Angular damping coefficient in all three directions.

dR

-

When checked (true) the joint will use the displacement (translational and rotational) between frame_a and frame_b at the initial or activation time as the spring offsets.

useInPlace

Keep Current

-

Options for how to select angle offsets when using .

 • Keep current: The relative angles between frame_a and frame_b at the instance of activation are used.
 • Reset to zero

setAngles