/GJOINT
Block Format Keyword Defines complex (geartype) joints. This keyword is not available for SPMD computation.
Format
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

/GJOINT/type/joint_ID/unit_ID  
joint_title  
node_ID_{0}  Fscale_{V}  Mass  Inertia  node_ID_{1}  node_ID_{2}  node_ID_{3}  
Mass_{1}  Inertia_{1}  r_{1x}  r_{1y}  r_{1z}  
Mass_{2}  Inertia_{2}  r_{2x}  r_{2y}  r_{2z}  
Mass_{3}  Inertia_{3}  r_{3x}  r_{3y}  r_{3z} 
Definition
Field  Contents  SI Unit Example 

type  Input type. (see table below for available keywords) 

joint_ID  Gear type joint
identifier. (Integer, maximum 10 digits) 

unit_ID  Unit Identifier. (Integer, maximum 10 digits) 

joint_title  Gear type joint
title. (Character, maximum 100 characters) 

node_ID_{0}  Primary node. identifier
(position node). (Integer) 

Fscale_{V}  Velocity scale
factor. Default = 1.0 (Real) 
$\left[\frac{\text{m}}{\text{s}}\right]$ 
Mass  Added mass to primary
node. Default = 0.0 (Real) 
$\left[\text{kg}\right]$ 
Inertia  Added to primary node
inertia. Default = 0.0 (Real) 
$\left[\text{kg}\cdot {\text{m}}^{\text{2}}\right]$ 
node_ID_{1}  Node identifier N_{1}. (Integer) 

node_ID_{2}  Node identifier N_{2}. (Integer) 

node_ID_{3}  Node identifier N_{3}  only necessary for differential gear
joint. (Integer) 

Mass_{1}  Added mass to node_ID_{1}. Default = 0.0 (Real) 
$\left[\text{kg}\right]$ 
Inertia_{1}  Added to node_ID_{1} inertia. Default = 0.0 (Real) 
$\left[\text{kg}\cdot {\text{m}}^{\text{2}}\right]$ ] 
r_{1x}  Local axis X
component. Default = 1.0 (Real) 

r_{1y}  Local axis Y
component. Default = 0.0 (Real) 

r_{1z}  Local axis Z
component. Default = 0.0 (Real) 

Mass_{2}  Added mass to node_ID_{2}. Default = 0.0 (Real) 
$\left[\text{kg}\right]$ 
Inertia  Added to node_ID_{2} inertia. Default = 0.0 (Real) 
$\left[\text{kg}\cdot {\text{m}}^{\text{2}}\right]$ ] 
r_{2x}  Local axis X
component. Default = 1.0 (Real) 

r_{2y}  Local axis Y
component. Default = 0.0 (Real) 

r_{2z}  Local axis Z
component. Default = 0.0 (Real) 

Mass_{3}  Added mass to node_ID_{3}. Default = 0.0 (Real) 
$\left[\text{kg}\right]$ 
Inertia_{3}  Added to node_ID_{3} inertia. Default = 0.0 (Real) 
$\left[\text{kg}\cdot {\text{m}}^{\text{2}}\right]$ ] 
r_{3x}  Local axis X
component. Default = 1.0 (Real) 

r_{3y}  Local axis Y
component. Default = 0.0 (Real) 

r_{3z}  Local axis Z
component. Default = 0.0 (Real) 
Complex Joint Types
 Type
 Description
 GEAR
 ∞ rotational gear
 DIFF
 ∞ differential gear
 RACK
 ∞ rack and pinion
Comments
 Complex (geartype) joints belong to the family of kinematic constraints treated by a Lagrange multipliers' method. A joint position is defined by a central node_ID_{0}, which are connected to two or three secondary nodes. Mass and inertia must be added to all nodes. It is advisable to place the primary node in the mass center of the joint. Kinematic constraints impose relations between secondary nodes velocities.
 Translational velocities of gear joint
nodes are constrained by a rigid link relation. For the rotational DOF, a scale
factor is imposed between velocities of node_ID_{1} and node_ID_{2}, measured in their local coordinates. The
corresponding constraint equations are:
(1) $$\alpha \left(\text{\Delta}{\omega}_{1}\cdot {r}_{1}\right)+\left(\text{\Delta}{\omega}_{2}\cdot {r}_{2}\right)=0$$(2) $$\left(\text{\Delta}{\omega}_{1}\cdot {s}_{1}\right)=0$$(3) $$\left(\text{\Delta}{\omega}_{1}\cdot {t}_{1}\right)=0$$(4) $$\left(\text{\Delta}{\omega}_{2}\cdot {s}_{2}\right)=0$$(5) $$\left(\text{\Delta}{\omega}_{2}\cdot {t}_{2}\right)=0$$Where, $\text{\Delta}{\omega}_{1}={\omega}_{1}{\omega}_{0}$ and $\text{\Delta}{\omega}_{2}={\omega}_{2}{\omega}_{0}$ are relative rotational velocities of node_ID_{1} and node_ID_{2} with respect to the rigid body rotational velocity.  The rotational velocities of a
differential gear joint are constrained by the relations:
(6) $$\alpha \left(\text{\Delta}{\omega}_{1}\cdot {r}_{1}\right)+\left(\text{\Delta}{\omega}_{2}\cdot {r}_{2}\right)+\left(\text{\Delta}{\omega}_{3}\cdot {r}_{3}\right)=0$$(7) $$\alpha \left(\text{\Delta}{\omega}_{1}\cdot {s}_{1}\right)+\left(\text{\Delta}{\omega}_{2}\cdot {s}_{2}\right)+\left(\text{\Delta}{\omega}_{3}\cdot {s}_{3}\right)=0$$(8) $$\alpha \left(\text{\Delta}{\omega}_{1}\cdot {t}_{1}\right)+\left(\text{\Delta}{\omega}_{2}\cdot {t}_{2}\right)+\left(\text{\Delta}{\omega}_{3}\cdot {t}_{3}\right)=0$$  The rack and pinion joint allows the
rotational velocity of node_ID_{1} to be transformed to a translational
velocity of node_ID_{2}. The constraint equations for these
velocities are:
(9) $$\alpha \left(\text{\Delta}{\omega}_{1}\cdot {r}_{1}\right)+\left(\text{\Delta}{V}_{2}\cdot {r}_{2}\right)=0$$(10) $$\alpha \left(\text{\Delta}{\omega}_{1}\cdot {s}_{1}\right)+\left(\text{\Delta}{V}_{2}\cdot {s}_{2}\right)=0$$(11) $$\alpha \left(\text{\Delta}{\omega}_{1}\cdot {t}_{1}\right)+\left(\text{\Delta}{V}_{2}\cdot {t}_{2}\right)=0$$  The node_ID_{3} is only necessary for a differential gear joint.
 This option is not available, if it is
applied on:
 a node with a null mass
 a node with a null inertia (except in case of node_ID_{2} of a rack type GJOINT)