Create a Mechanism with Different Joints in MATLAB

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This example shows how to model a mechanism that contains different types of joints in MATLAB®. It also shows a way of setting operating point targets for the joint primitives of the joints.

Create a Multibody object and add the necessary components, such as WorldFrame and Gravity.

import simscape.Value simscape.multibody.*;

mb = Multibody;
addComponent(mb, 'World', WorldFrame());

sep = Value(20, 'cm'); % Separation between blocks

% Translucent ground plane
ground = Solid(Brick([[5 4] * sep, Value(1, 'cm')]), UniformDensity, ...
    SimpleVisualProperties(0.7 *[1 1 1], 0.6));
addComponent(mb, 'Ground', ground);
addComponent(mb, 'Ground_Pose', RigidTransform(CartesianTranslation([2 1.5 0] * sep)));
connectVia(mb, 'Ground_Pose', 'World/W', 'Ground/R');

% Zero gravity
mb.Gravity = Value([0 0 0], 'm/s^2');

Add different types of joints to the Multibody object using the custom function addJoint.

% Row 1:  Single-primitive joints
addJoint(mb, 'Revolute',         [0 0] * sep,   [1 0 0]);
addJoint(mb, 'Prismatic',        [1 0] * sep,   [1 1 0]);
addJoint(mb, 'Spherical',        [2 0] * sep,   [0 .8 0]);
addJoint(mb, 'LeadScrew',        [3 0] * sep,   [0 0 .9]);
addJoint(mb, 'ConstantVelocity', [4 0] * sep,   [.8 0 .8]);

% Row 2:  2-DOF multi-primitive joints
addJoint(mb, 'Universal',        [0.5 1] * sep, [.95 .4 0]);
addJoint(mb, 'Rectangular',      [1.5 1] * sep, [.4 .9 0]);
addJoint(mb, 'Cylindrical',      [2.5 1] * sep, [0 .7 .7]);
addJoint(mb, 'PinSlot',          [3.5 1] * sep, [.6 0 1]);

% Row 3:  3-DOF and 4-DOF multi-primitive joints
addJoint(mb, 'Gimbal',           [0 2] * sep,   [.37 .86 .57]);
addJoint(mb, 'Cartesian',        [1 2] * sep,   [.28 .55 .96]);
addJoint(mb, 'Planar',           [2 2] * sep,   [.91 .63 .10]);
addJoint(mb, 'Bearing',          [3 2] * sep,   [.96 .49 .80]);
addJoint(mb, 'Telescoping',      [4 2] * sep,   [.8 .8 .5]);

% Row 4:  0-DOF and 6-DOF joints
addJoint(mb, 'Weld',             [1 3] * sep,   .1 * [1 1 1]);
addJoint(mb, 'Bushing',          [2 3] * sep,   .8 * [1 1 1]);
addJoint(mb, 'SixDof',           [3 3] * sep,    1 * [1 1 1]);

To create operating points that specify the position or velocity targets of a joint, get the path to each of the joint primitives. The Multibody object provides a method jointPrimitivePaths to list the paths to all the joint primitives in the mechanism. Use this list as one of the inputs to the custom function randomOpPoint that creates an operating point specifying random velocities for all the joints.

jointPrimPaths = jointPrimitivePaths(mb);
op = randomOpPoint(jointPrimPaths, Value(90, 'deg/s'), Value(1, 'cm/s'));

After you create the operating point, compile the Multibody object and use the computeState method to view if the above random velocity targets are achieved.

cmb = compile(mb);
state = computeState(cmb,op)

state = 
  State:

  Status: Valid

  Assembly diagnostics:
  x
    Revolute_Joint
        Joint successfully assembled
        Rz
            Free position value: +0 (deg)
            High priority velocity target +23.5864 (deg/s) achieved
    Prismatic_Joint
        Joint successfully assembled
        Pz
            Free position value: +0 (m)
            High priority velocity target +0.210897 (cm/s) achieved
    Spherical_Joint
        Joint successfully assembled
        S
            Free position value: [+0 +0 +0], +0 (deg)
            High priority velocity target [-80.4494 -62.6214 -85.1939] (deg/s) achieved
    LeadScrew_Joint
        Joint successfully assembled
        LSz
            Free position value: +0 (deg)
            High priority velocity target +0.0848914 (cm/s) achieved
    ConstantVelocity_Joint
        Joint successfully assembled
        CV
            High priority position target +90 (deg) achieved
            High priority velocity target [-5 +10] (deg/s) achieved
    Universal_Joint
        Joint successfully assembled
        Rx
            Free position value: +0 (deg)
            High priority velocity target +73.9708 (deg/s) achieved
        Ry
            Free position value: +0 (deg)
            High priority velocity target +10.0194 (deg/s) achieved
    Rectangular_Joint
        Joint successfully assembled
        Px
            Free position value: +0 (m)
            High priority velocity target +0.162366 (cm/s) achieved
        Py
            Free position value: +0 (m)
            High priority velocity target +0.00724535 (cm/s) achieved
    Cylindrical_Joint
        Joint successfully assembled
        Rz
            Free position value: +0 (deg)
            High priority velocity target -12.8893 (deg/s) achieved
        Pz
            Free position value: +0 (m)
            High priority velocity target +0.984314 (cm/s) achieved
    PinSlot_Joint
        Joint successfully assembled
        Px
            Free position value: +0 (m)
            High priority velocity target +0.454274 (cm/s) achieved
        Rz
            Free position value: +0 (deg)
            High priority velocity target +21.4513 (deg/s) achieved
    Gimbal_Joint
        Joint successfully assembled
        Rx
            Free position value: +0 (deg)
            High priority velocity target +89.4072 (deg/s) achieved
        Ry
            Free position value: +0 (deg)
            High priority velocity target +28.0298 (deg/s) achieved
        Rz
            Free position value: +0 (deg)
            High priority velocity target +25.9604 (deg/s) achieved
    Cartesian_Joint
        Joint successfully assembled
        Px
            Free position value: +0 (m)
            High priority velocity target -0.25679 (cm/s) achieved
        Py
            Free position value: +0 (m)
            High priority velocity target -0.640975 (cm/s) achieved
        Pz
            Free position value: +0 (m)
            High priority velocity target +0.594411 (cm/s) achieved
    Planar_Joint
        Joint successfully assembled
        Px
            Free position value: +0 (m)
            High priority velocity target +0.433686 (cm/s) achieved
        Py
            Free position value: +0 (m)
            High priority velocity target +0.215342 (cm/s) achieved
        Rz
            Free position value: +0 (deg)
            High priority velocity target -60.8224 (deg/s) achieved
    Bearing_Joint
        Joint successfully assembled
        Pz
            Free position value: +0 (m)
            High priority velocity target +0.908122 (cm/s) achieved
        Rx
            Free position value: +0 (deg)
            High priority velocity target +2.55215 (deg/s) achieved
        Ry
            Free position value: +0 (deg)
            High priority velocity target -63.2583 (deg/s) achieved
        Rz
            Free position value: +0 (deg)
            High priority velocity target -63.7585 (deg/s) achieved
    Telescoping_Joint
        Joint successfully assembled
        S
            Free position value: [+0 +0 +0], +0 (deg)
            High priority velocity target [-89.3162 -43.8057 -52.8736] (deg/s) achieved
        Pz
            Free position value: +0 (m)
            High priority velocity target -0.844793 (cm/s) achieved
    Weld_Joint
        Joint successfully assembled
    Bushing_Joint
        Joint successfully assembled
        Px
            Free position value: +0 (m)
            High priority velocity target +0.66129 (cm/s) achieved
        Py
            Free position value: +0 (m)
            High priority velocity target +0.148752 (cm/s) achieved
        Pz
            Free position value: +0 (m)
            High priority velocity target -0.792454 (cm/s) achieved
        Rx
            Free position value: +0 (deg)
            High priority velocity target -44.7294 (deg/s) achieved
        Ry
            Free position value: +0 (deg)
            High priority velocity target -32.5625 (deg/s) achieved
        Rz
            Free position value: +0 (deg)
            High priority velocity target -71.8616 (deg/s) achieved
    SixDof_Joint
        Joint successfully assembled
        Px
            Free position value: +0 (m)
            High priority velocity target +0.664527 (cm/s) achieved
        Py
            Free position value: +0 (m)
            High priority velocity target -0.294531 (cm/s) achieved
        Pz
            Free position value: +0 (m)
            High priority velocity target -0.806505 (cm/s) achieved
        S
            Free position value: [+0 +0 +0], +0 (deg)
            High priority velocity target [-24.8307 -63.8315 -74.1798] (deg/s) achieved

To perform any simulation workflows, generate the Simulink® model of the mechanism by using the makeBlockDiagram method.

makeBlockDiagram(mb,op,'jointZooModel');

Create a Mechanism with Different Joints in MATLAB

See Also