/GJOINT

Block Format Keyword Defines complex (gear-type) 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_ID0 FscaleV Mass Inertia node_ID1 node_ID2 node_ID3
Mass1 Inertia1 r1x r1y r1z
Mass2 Inertia2 r2x r2y r2z
Mass3 Inertia3 r3x r3y r3z

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_ID0 Primary node. identifier (position node).

(Integer)

 
FscaleV Velocity scale factor.

Default = 1.0 (Real)

[ m s ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaada Wcaaqaaiaab2gaaeaacaqGZbaaaaGaay5waiaaw2faaaaa@39DE@
Mass Added mass to primary node.

Default = 0.0 (Real)

[ kg ]
Inertia Added to primary node inertia.

Default = 0.0 (Real)

[ kg m 2 ]
node_ID1 Node identifier N1.

(Integer)

 
node_ID2 Node identifier N2.

(Integer)

 
node_ID3 Node identifier N3 - only necessary for differential gear joint.

(Integer)

 
Mass1 Added mass to node_ID1.

Default = 0.0 (Real)

[ kg ]
Inertia1 Added to node_ID1 inertia.

Default = 0.0 (Real)

[ kg m 2 ] ]
r1x Local axis X component.

Default = 1.0 (Real)

 
r1y Local axis Y component.

Default = 0.0 (Real)

 
r1z Local axis Z component.

Default = 0.0 (Real)

 
Mass2 Added mass to node_ID2.

Default = 0.0 (Real)

[ kg ]
Inertia Added to node_ID2 inertia.

Default = 0.0 (Real)

[ kg m 2 ] ]
r2x Local axis X component.

Default = 1.0 (Real)

 
r2y Local axis Y component.

Default = 0.0 (Real)

 
r2z Local axis Z component.

Default = 0.0 (Real)

 
Mass3 Added mass to node_ID3.

Default = 0.0 (Real)

[ kg ]
Inertia3 Added to node_ID3 inertia.

Default = 0.0 (Real)

[ kg m 2 ] ]
r3x Local axis X component.

Default = 1.0 (Real)

 
r3y Local axis Y component.

Default = 0.0 (Real)

 
r3z Local axis Z component.

Default = 0.0 (Real)

 

Complex Joint Types

Type
Description
GEAR
∞ rotational gear
DIFF
∞ differential gear
RACK
∞ rack and pinion

Comments

  1. Complex (gear-type) joints belong to the family of kinematic constraints treated by a Lagrange multipliers' method. A joint position is defined by a central node_ID0, 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.

    clip0016-1
    Figure 1.
  2. 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_ID1 and node_ID2, measured in their local coordinates. The corresponding constraint equations are:(1)
    α ( Δ ω 1 r 1 ) + ( Δ ω 2 r 2 ) = 0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqySde2aae WaaeaacqqHuoarcaWHjpWaaSbaaSqaaiaaigdaaeqaaOGaeyyXICTa aCOCamaaBaaaleaacaaIXaaabeaaaOGaayjkaiaawMcaaiabgUcaRm aabmaabaGaeuiLdqKaaCyYdmaaBaaaleaacaaIYaaabeaakiabgwSi xlaahkhadaWgaaWcbaGaaGOmaaqabaaakiaawIcacaGLPaaacqGH9a qpcaaIWaaaaa@4D10@
    (2)
    ( Δ ω 1 s 1 ) = 0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaeWaaeaacq qHuoarcaWHjpWaaSbaaSqaaiaaigdaaeqaaOGaeyyXICTaaC4Camaa BaaaleaacaaIXaaabeaaaOGaayjkaiaawMcaaiabg2da9iaaicdaaa a@4123@
    (3)
    ( Δ ω 1 t 1 ) = 0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaeWaaeaacq qHuoarcaWHjpWaaSbaaSqaaiaaigdaaeqaaOGaeyyXICTaaCiDamaa BaaaleaacaaIXaaabeaaaOGaayjkaiaawMcaaiabg2da9iaaicdaaa a@4124@
    (4)
    ( Δ ω 2 s 2 ) = 0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaeWaaeaacq qHuoarcaWHjpWaaSbaaSqaaiaaikdaaeqaaOGaeyyXICTaaC4Camaa BaaaleaacaaIYaaabeaaaOGaayjkaiaawMcaaiabg2da9iaaicdaaa a@4125@
    (5)
    ( Δ ω 2 t 2 ) = 0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaeWaaeaacq qHuoarcaWHjpWaaSbaaSqaaiaaikdaaeqaaOGaeyyXICTaaCiDamaa BaaaleaacaaIYaaabeaaaOGaayjkaiaawMcaaiabg2da9iaaicdaaa a@4126@
    Where, Δ ω 1 = ω 1 ω 0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeuiLdqKaaC yYdmaaBaaaleaacaaIXaaabeaakiabg2da9iaahM8adaWgaaWcbaGa aGymaaqabaGccqGHsislcaWHjpWaaSbaaSqaaiaaicdaaeqaaaaa@4017@ and Δ ω 2 = ω 2 ω 0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeuiLdqKaaC yYdmaaBaaaleaacaaIYaaabeaakiabg2da9iaahM8adaWgaaWcbaGa aGOmaaqabaGccqGHsislcaWHjpWaaSbaaSqaaiaaicdaaeqaaaaa@4019@ are relative rotational velocities of node_ID1 and node_ID2 with respect to the rigid body rotational velocity.

    clip0017
    Figure 2.
  3. The rotational velocities of a differential gear joint are constrained by the relations:(6)
    α ( Δ ω 1 r 1 ) + ( Δ ω 2 r 2 ) + ( Δ ω 3 r 3 ) = 0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqySde2aae WaaeaacqqHuoarcaWHjpWaaSbaaSqaaiaaigdaaeqaaOGaeyyXICTa aCOCamaaBaaaleaacaaIXaaabeaaaOGaayjkaiaawMcaaiabgUcaRm aabmaabaGaeuiLdqKaaCyYdmaaBaaaleaacaaIYaaabeaakiabgwSi xlaahkhadaWgaaWcbaGaaGOmaaqabaaakiaawIcacaGLPaaacqGHRa Wkdaqadaqaaiabfs5aejaahM8adaWgaaWcbaGaaG4maaqabaGccqGH flY1caWHYbWaaSbaaSqaaiaaiodaaeqaaaGccaGLOaGaayzkaaGaey ypa0JaaGimaaaa@5761@
    (7)
    α ( Δ ω 1 s 1 ) + ( Δ ω 2 s 2 ) + ( Δ ω 3 s 3 ) = 0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqySde2aae WaaeaacqqHuoarcaWHjpWaaSbaaSqaaiaaigdaaeqaaOGaeyyXICTa aC4CamaaBaaaleaacaaIXaaabeaaaOGaayjkaiaawMcaaiabgUcaRm aabmaabaGaeuiLdqKaaCyYdmaaBaaaleaacaaIYaaabeaakiabgwSi xlaahohadaWgaaWcbaGaaGOmaaqabaaakiaawIcacaGLPaaacqGHRa Wkdaqadaqaaiabfs5aejaahM8adaWgaaWcbaGaaG4maaqabaGccqGH flY1caWHZbWaaSbaaSqaaiaaiodaaeqaaaGccaGLOaGaayzkaaGaey ypa0JaaGimaaaa@5764@
    (8)
    α ( Δ ω 1 t 1 ) + ( Δ ω 2 t 2 ) + ( Δ ω 3 t 3 ) = 0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqySde2aae WaaeaacqqHuoarcaWHjpWaaSbaaSqaaiaaigdaaeqaaOGaeyyXICTa aCiDamaaBaaaleaacaaIXaaabeaaaOGaayjkaiaawMcaaiabgUcaRm aabmaabaGaeuiLdqKaaCyYdmaaBaaaleaacaaIYaaabeaakiabgwSi xlaahshadaWgaaWcbaGaaGOmaaqabaaakiaawIcacaGLPaaacqGHRa Wkdaqadaqaaiabfs5aejaahM8adaWgaaWcbaGaaG4maaqabaGccqGH flY1caWH0bWaaSbaaSqaaiaaiodaaeqaaaGccaGLOaGaayzkaaGaey ypa0JaaGimaaaa@5767@

    clip0018
    Figure 3.
  4. The rack and pinion joint allows the rotational velocity of node_ID1 to be transformed to a translational velocity of node_ID2. The constraint equations for these velocities are:(9)
    α ( Δ ω 1 r 1 ) + ( Δ V 2 r 2 ) = 0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqySde2aae WaaeaacqqHuoarcaWHjpWaaSbaaSqaaiaaigdaaeqaaOGaeyyXICTa aCOCamaaBaaaleaacaaIXaaabeaaaOGaayjkaiaawMcaaiabgUcaRm aabmaabaGaeuiLdqKaaCOvamaaBaaaleaacaaIYaaabeaakiabgwSi xlaahkhadaWgaaWcbaGaaGOmaaqabaaakiaawIcacaGLPaaacqGH9a qpcaaIWaaaaa@4C9A@
    (10)
    α ( Δ ω 1 s 1 ) + ( Δ V 2 s 2 ) = 0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqySde2aae WaaeaacqqHuoarcaWHjpWaaSbaaSqaaiaaigdaaeqaaOGaeyyXICTa aC4CamaaBaaaleaacaaIXaaabeaaaOGaayjkaiaawMcaaiabgUcaRm aabmaabaGaeuiLdqKaaCOvamaaBaaaleaacaaIYaaabeaakiabgwSi xlaahohadaWgaaWcbaGaaGOmaaqabaaakiaawIcacaGLPaaacqGH9a qpcaaIWaaaaa@4C9C@
    (11)
    α ( Δ ω 1 t 1 ) + ( Δ V 2 t 2 ) = 0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqySde2aae WaaeaacqqHuoarcaWHjpWaaSbaaSqaaiaaigdaaeqaaOGaeyyXICTa aCiDamaaBaaaleaacaaIXaaabeaaaOGaayjkaiaawMcaaiabgUcaRm aabmaabaGaeuiLdqKaaCOvamaaBaaaleaacaaIYaaabeaakiabgwSi xlaahshadaWgaaWcbaGaaGOmaaqabaaakiaawIcacaGLPaaacqGH9a qpcaaIWaaaaa@4C9E@
  5. The node_ID3 is only necessary for a differential gear joint.
  6. 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_ID2 of a rack type GJOINT)