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(testmodels-kinematictreeprismaticjacobiantest)=
# kinematicTreePrismaticJacobianTest.py

You can view and download this file on Github: [kinematicTreePrismaticJacobianTest.py](https://github.com/jgerstmayr/EXUDYN/tree/master/python/TestModels/kinematicTreePrismaticJacobianTest.py)

```{code-block} python
:linenos:

#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
# This is an EXUDYN example
#
# Details:  The position Jacobian of a prismatic joint of ObjectKinematicTree in a rotated joint frame,
#           tested through a force on a MarkerKinematicTreeRigid (#2740). A prismatic link is rotated
#           either by a revolute parent link or by its joint transformation; a force of 1 N along
#           the prismatic axis accelerates a mass of 2 kg by 0.5 m/s^2, so q1 = 0.25 after 1 s in
#           every case - as long as the Jacobian column is the global axis.
#
# Author:   Johannes Gerstmayr
# Date:     2026-09-29
#
# Copyright:This file is part of Exudyn. Exudyn is free software. You can redistribute it and/or modify it under the terms of the Exudyn license. See 'LICENSE.txt' for more details.
#
#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

import exudyn as exu
from exudyn.utilities import * #includes itemInterface and rigidBodyUtilities

import numpy as np

testIsActive = exu.sys.get('testIsActive', False)

SC = exu.SystemContainer()
mbs = SC.AddSystem()

mass = 2        #mass of the prismatic link
force = 1       #force along the prismatic axis
testResult = 0

#(angle of the revolute parent link, rotation of the prismatic joint frame about z)
cases = [(0, 0), (0.25*np.pi, 0), (0.5*np.pi, 0), (0, 0.5*np.pi), (0.5*np.pi, 0.25*np.pi)]
for (q0, alpha) in cases:
    mbs.Reset()
    nGeneric = mbs.AddNode(NodeGenericODE2(referenceCoordinates=[0.,0.], initialCoordinates=[q0,0.],
                                           initialCoordinates_t=[0.,0.], numberOfODE2Coordinates=2))
    #link 0: revolute about z, held by a huge inertia; link 1: prismatic along the x-axis of its joint frame
    oKT = mbs.AddObject(ObjectKinematicTree(nodeNumber=nGeneric,
                                            jointTypes=[exu.JointType.RevoluteZ, exu.JointType.PrismaticX],
                                            linkParents=[-1, 0],
                                            jointTransformations=exu.Matrix3DList([np.eye(3), RotationMatrixZ(alpha)]),
                                            jointOffsets=exu.Vector3DList([[0,0,0], [0,0,0]]),
                                            linkInertiasCOM=exu.Matrix3DList([1e8*np.eye(3), np.eye(3)]),
                                            linkCOMs=exu.Vector3DList([[0,0,0], [0,0,0]]),
                                            linkMasses=[1e8, mass]))
    mLink1 = mbs.AddMarker(MarkerKinematicTreeRigid(objectNumber=oKT, linkNumber=1, localPosition=[0,0,0]))
    #the prismatic axis in the global frame; its line passes through the revolute axis, so no torque on link 0
    axis = RotationMatrixZ(q0 + alpha) @ np.array([1,0,0])
    mbs.AddLoad(LoadForceVector(markerNumber=mLink1, loadVector=force*axis))

    mbs.Assemble()
    simulationSettings = exu.SimulationSettings()
    simulationSettings.timeIntegration.numberOfSteps = 100
    simulationSettings.timeIntegration.endTime = 1
    simulationSettings.solution.file.write = not testIsActive
    mbs.SolveDynamic(simulationSettings)

    q = mbs.GetNodeOutput(nGeneric, exu.OutputVariableType.Coordinates)
    exu.Print('q0 =', round(q0, 4), ', alpha =', round(alpha, 4), ': q1 =', q[1], '(expected 0.25)')
    testResult += q[1]

#5 cases of 0.25
exu.Print('solution of kinematicTreePrismaticJacobianTest=', testResult)
exu.sys['testResult'] = testResult
```