MarkerBodiesRelativeTranslationCoordinate

A coordinate-based Marker attached to two rigid bodies or beams which computes the relative translation between the bodies according to the given axis. This marker can be used together with coordinate-based constraints and connectors (e.g., CoordinateSpringDamper and CoordinateConstraint). NOTE: it is assumed that the two bodies can only move along the given axis (e.g., constrained by a prismatic joint) – otherwise results may be unexpected. NOTE: this approach is not compatible with FFRF-based flexible bodies and currently requires and intermediate rigid body.

Interface

Provides: Coordinate
Connectors, constraints and loads that can use it: ObjectConnectorCoordinateSpringDamper, ObjectConnectorCoordinateSpringDamperExt, ObjectConnectorCoordinate, ObjectContactCoordinate, LoadCoordinate

Parameters

The parameters of the item; in a dictionary, its type is ‘BodiesRelativeTranslationCoordinate’:

name	type	size	default	description
name	String		‘’	marker’s unique name
bodyNumbers	ArrayObjectIndex		[ invalid (-1), invalid (-1) ]	(symbol: \([b_0,b_1]\tp\)) list of body numbers for which relative coordinate is computed
localPosition0	Vector3D	3	[0.,0.,0.]	(symbol: \(\LU{m_0}{\pv}_0\)) local position on body 0; i.e. local (body-fixed) position where position is measured and force is applied to
localPosition1	Vector3D	3	[0.,0.,0.]	(symbol: \(\LU{m_1}{\pv}_1\)) local position on body 1; i.e. local (body-fixed) position where position is measured and force is applied to
axis0	Vector3D	3	[1.,0.,0.]	(symbol: \(\LU{m_0}{\av}_0\)) axis defined in body 0, along which the relative translation is measured
offset	Real		0.	(symbol: \(x_\mathrm{off}\)) translation offset [SI:m] subtracted from the translation; can be used to change the zero position
visualization	VMarkerBodiesRelativeTranslationCoordinate			parameters for visualization of item

Visualization parameters

The parameters of VMarkerBodiesRelativeTranslationCoordinate, given as visualization:

name	type	size	default	description
show	Bool		True	set true, if item is shown in visualization and false if it is not shown

Drawing

Drawn as all markers.

Detailed description

The marker consists of two bodies, body \(b_0\) and body \(b_1\) with respective global marker positions \(\LU{0}{\pv}_{m0}\) and \(\LU{0}{\pv}_{m1}\), depending on local positions \(\LU{m_0}{\pv}_0\) and \(\LU{m_1}{\pv}_1\), and marker orientations \(\LU{0,m_0}{\Rot}_{m0}\) and \(\LU{0,m_1}{\Rot}_{m1}\). The global axis is computed as

\[ \LU{0}{\av}_0 = \LU{0,m_0}{\Rot}_{m0} \LU{m_0}{\av}_0 \]

The relative translation marker computes the relative translation from the equation

\[ t = \LU{0}{\av}_0\tp (\pv_{m1} - \pv_{m0}) - x_\mathrm{off} \]

The translational velocity, which may be used in coordinate spring-dampers or for velocity-level constraints, is computed as

\[ \dot t = \LU{0}{\av}_0\tp (\dot \pv_{m1} - \dot \pv_{m0}) + \LU{0}{\dot \av}_0\tp (\pv_{m1} - \pv_{m0}) \]

Jacobians are computed according to the relative translational velocity, ignoring the \(\dot \av_0\) part. Using this approach, coordinate constraints can be added to mechanisms to purely add internal drives, not affecting global momenta. Furthermore, coupling to a relative rotation marker MarkerBodiesRelativeRotationCoordinate can be used to create advanced mechanisms and gears.

It is a coordinate marker: coordinate connectors, coordinate constraints and LoadCoordinate use it. Body 0 must provide position and orientation, body 1 a position, both at a local point - a rigid body, and for body 1 also a mass point; Assemble() refuses other bodies.

Mini example

#the translation of body 1 relative to body 0 along an axis of body 0, held by a coordinate constraint
inertia = InertiaCuboid(density=1000, sideLengths=[0.4,0.2,0.1])
node = mbs.AddNode(NodeRigidBodyRxyz(referenceCoordinates=[0,0,0, 0,0,0]))
body = mbs.AddObject(ObjectRigidBody(nodeNumber=node, mass=inertia.Mass(),
                                     inertia=inertia.GetInertia6D()))
mRel = mbs.AddMarker(MarkerBodiesRelativeTranslationCoordinate(bodyNumbers=[oGround, body], axis0=[1,0,0]))
mGround = mbs.AddMarker(MarkerNodeCoordinate(nodeNumber=nGround, coordinate=0))
mbs.AddObject(ObjectConnectorCoordinate(markerNumbers=[mGround, mRel], offset=0.3))

mbs.Assemble()
mbs.SolveDynamic()

#the body is held 0.3 along x of the ground
exu.sys['testResult'] = mbs.GetNodeOutput(node, exu.OutputVariableType.Position)[0] #0.3

Relevant Examples (Ex) and TestModels (TM) with weblink to github: involuteGearGraphics.py (Ex), relativeRotationTranslationMechanism.py (TM)