Gearbox

This example models a gearbox in two different ways:

Using the 3D GearConstraint component from the Multibody library.
Using the 1D IdealGear component from the Rotational submodule, together with a Mounting1D component.

The GearConstraint has two rotational axes which do not have to be parallel. If wou want to select rotational axes, use the keyword arguments n_a and n_b to GearConstraint.

using Multibody
using ModelingToolkit
using Plots
using JuliaSimCompiler
using OrdinaryDiffEq

t = Multibody.t
D = Differential(t)
world = Multibody.world

systems = @named begin
    gearConstraint = GearConstraint(; ratio = 10)
    cyl1 = Body(; m = 1, r_cm = [0.4, 0, 0])
    cyl2 = Body(; m = 1, r_cm = [0.4, 0, 0])
    torque1 = Torque(resolve_frame = :frame_b)
    fixed = Fixed()
    inertia1 = Rotational.Inertia(J = cyl1.I_11)
    idealGear = Rotational.IdealGear(ratio = 10, use_support = true)
    inertia2 = Rotational.Inertia(J = cyl2.I_11)
    torque2 = Rotational.Torque(use_support = true)
    mounting1D = Mounting1D()
end

eqs = [connect(world.frame_b, gearConstraint.bearing)
       connect(cyl1.frame_a, gearConstraint.frame_a)
       connect(gearConstraint.frame_b, cyl2.frame_a)
       connect(torque1.frame_b, cyl1.frame_a)
       connect(torque1.frame_a, world.frame_b)
       # connect(sine.output, torque1.torque)
       torque1.torque.u .~ [2sin(t), 0, 0]
       connect(inertia1.flange_b, idealGear.flange_a)
       connect(idealGear.flange_b, inertia2.flange_a)
       connect(torque2.flange, inertia1.flange_a)
       # connect(sine.output, torque2.tau)
       torque2.tau.u ~ 2sin(t)
       connect(mounting1D.flange_b, idealGear.support)
       connect(mounting1D.flange_b, torque2.support)
       connect(fixed.frame_b, mounting1D.frame_a)]

@named model = ODESystem(eqs, t, systems = [world; systems])
cm = complete(model)
ssys = structural_simplify(multibody(model))
prob = ODEProblem(ssys, [
    D(cm.idealGear.phi_b) => 0
    cm.idealGear.phi_b => 0
], (0, 10))
sol = solve(prob, Rodas4())
plot(sol, idxs=[
    inertia1.phi
    inertia2.phi
    gearConstraint.actuatedRevolute_a.phi
    gearConstraint.phi_b
    inertia1.phi / inertia2.phi # One can plot arbitrary expressions of variables! In this case, we plot the ratio between the two angles.
], layout=3, sp=[1 2 1 2 3], framestyle=:zerolines)

The plot indicates that the ratio between the angles of inertia 1 and 2 is 10, as expected, and that the same ratio holds between the two sides of the 3D gear constraint.