BGMod Documentation / v3
BGMod handbook

Translational mechanics

Component reference · matches the Elements library.

Translational mechanics → Primitives / AdvancedForce [N]Velocity [m/s]

Translational mechanics: effort is force and flow is velocity. A spring uses compliance C = 1/k; I represents mass.

Primitives

Expand a component for its equation, parameters and initial state. Defaults match insertion from the library.

0Common forceEqual force; signed velocities balance.

Equal force; signed velocities balance.

Ports: p1, p2, …

F₁ = F₂ = …; Σ v_local = 0
Parameters
No coefficient or stored state. At least two connected bonds. Junction endpoint signs follow the connection order; reversing a power arrow does not rewire it.
Defaults
—
Classic element 0Classic junction; three bonds are shown, but the number of ports can vary.0p1p2p3
Classic junction; three bonds are shown, but the number of ports can vary. Causal strokes are omitted; see notation and signs.
1Common velocityCommon reference velocity; signed forces balance.

Common reference velocity; signed forces balance.

Ports: p1, p2, …

directionᵢ · vᵢ = v_ref; Σ sᵢ Fᵢ = 0
Parameters
No coefficient or stored state. At least two connected bonds. Junction endpoint signs follow the connection order; reversing a power arrow does not rewire it.
Defaults
—
Classic element 1Classic junction; three bonds are shown, but the number of ports can vary.1p1p2p3
Classic junction; three bonds are shown, but the number of ports can vary. Causal strokes are omitted; see notation and signs.
RDamperViscous damper with constant damping coefficient b.N·s/m

Viscous damper with constant damping coefficient b.

Ports: M

F = b v_local; P_loss = b v_local²
Parameters
value > 0; constant linear coefficient.
Defaults
value = 1 · N·s/m
Classic element RClassic one-port element with no further internal graph. One bond carries effort and flow relative to the domain reference.MRe, f
Classic one-port element with no further internal graph. One bond carries effort and flow relative to the domain reference. Causal strokes are omitted; see notation and signs.
CSpring complianceLinear spring expressed as compliance C = 1/k.m/N

Linear spring expressed as compliance C = 1/k.

Ports: M

dx/dt = v_local; F = x/C = kx; E = x²/(2C)
Parameters
value > 0; constant linear coefficient. Enter compliance 1/k, not stiffness k.
Defaults
value = 0.01, initial = 0 · m/N
Initial state
Spring extension x₀ [m]; x₀ = C·F₀. initial = 0.
Classic element CClassic one-port element with no further internal graph. One bond carries effort and flow relative to the domain reference.MCe, f
Classic one-port element with no further internal graph. One bond carries effort and flow relative to the domain reference. Causal strokes are omitted; see notation and signs.
IMassTranslational mass m; stores mechanical momentum.kg

Translational mass m; stores mechanical momentum.

Ports: M

dp/dt = F; v_local = p/m; E = p²/(2m)
Parameters
value > 0; constant linear coefficient.
Defaults
value = 1, initial = 0 · kg
Initial state
Momentum p₀ [kg·m/s]; p₀ = m·v_local(0), not initial velocity itself. initial = 0.
Classic element IClassic one-port element with no further internal graph. One bond carries effort and flow relative to the domain reference.MIe, f
Classic one-port element with no further internal graph. One bond carries effort and flow relative to the domain reference. Causal strokes are omitted; see notation and signs.
SeForce sourcePrescribed force; motion is determined by the network.N

Prescribed force; motion is determined by the network.

Ports: M

F = u(t)
Parameters
Constant: value. Step: value before time, after at and after time; time ≥ 0 s. Values may have either sign. No stored state.
Defaults
value = 1, waveform = constant · N
Classic element SeClassic one-port element with no further internal graph. One bond carries effort and flow relative to the domain reference.MSee, f
Classic one-port element with no further internal graph. One bond carries effort and flow relative to the domain reference. Causal strokes are omitted; see notation and signs.
SfVelocity sourcePrescribed velocity; reaction force comes from the network.m/s

Prescribed velocity; reaction force comes from the network.

Ports: M

v_local = −u(t)
Parameters
Constant: value. Step: value before time, after at and after time; time ≥ 0 s. Values may have either sign. No stored state. Positive input supplies flow out of the source, so inward local flow is negative.
Defaults
value = 0.1, waveform = constant · m/s
Classic element SfClassic one-port element with no further internal graph. One bond carries effort and flow relative to the domain reference.MSfe, f
Classic one-port element with no further internal graph. One bond carries effort and flow relative to the domain reference. Causal strokes are omitted; see notation and signs.
TFIdeal translational transformer1

Ports: P, S

FP = n·FS; vS_local = −n·vP_local
FP·vP_local + FS·vS_local = 0

P/S ports belong to the selected physical domain. Enter a finite dimensionless n > 0, default 1. Local flows enter both ports. With input at P and output at S, output effort is input effort / n and output flow is n × input flow. TF neither stores nor dissipates energy; exactly one port supplies effort.

Models an ideal lever or polyspast with a constant motion ratio. Choose positive axes separately, for example along the rope pull and upward for the load. Elasticity, friction and slack-rope behavior are excluded.

P → TF:n → S

Example, physical sketch and verification

Advanced

Actuators

Double-acting cylinderA: Hydraulics, B: Hydraulics, M: Translational mechanicsMultiphysics · shared referenceMass and loadM: Translational mechanics

Advanced membership follows exposed port domains. The cylinder appears in Hydraulics and Translational mechanics. The pump curve has no electrical port; the gas accumulator has no thermal port.