Howto:Animate gear scissors using the tracking animation

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A locked-track animation is an animation that can do exactly the same thing as the Locked Track constraint available in Blender. It is most commonly used to animate landing gear scissor (torque) links, but can also simulate any simple inverse kinematic system consisting of two rigid arms connected by a revolute joint (hinge).

How it works

A scissors linkage has two arms connected by a middle hinge. One arm is attached to the gear leg (fixed end); the other is attached to the oleo strut and moves with it as it compresses and extends. The locked-track animation automatically rotates both arms so the middle hinge stays connected throughout that travel.

One <animation> block handles both arms. No parenting or grouping of objects in the 3D file is required, the animation works purely by object name.

There are only two axes required: the lock-axis and the track-axis. They must be orthogonal. The lock-axis is the axis of the hinge pin (the axis rotation occurs around). The track-axis is the direction the arm initially points in the rest-position geometry. Internally the track-axis is always orthonormalized to the lock-axis, as calculations are always performed in the plane normal to the lock-axis.

Parameter reference

Parameter Meaning
object-name The upper scissor arm (attached to the gear leg)
center The hinge point where the upper arm attaches to the gear leg i.e. the upper arm's pivot point
target-name The object being tracked which is typically the oleo strut, since its position drives the animation
target-center The point on the target object that the upper arm tracks toward i.e. where the lower arm attaches to the oleo strut
lock-axis The direction the hinge pin points i.e. the axis the arms rotate around
track-axis Direction vector from center to target-center in the rest position (see below)
slave-name The lower scissor arm
slave-center The middle hinge point where the two arms meet

Getting coordinates from Blender

All coordinates can be read directly from vertex positions. Select the vertex at the point of interest, read global coordinates from the N-panel, and use them directly in the XML.

  1. center: select the vertex where the upper arm hinges on the gear leg
  2. target-center: select the vertex where the lower arm attaches to the oleo strut
  3. slave-center: select the vertex where the two arms meet in the middle
  4. track-axis: subtract center from target-center i.e. track-axis = target-center - center. Do not normalise it
  5. lock-axis: select the two vertices at either end of the hinge pin and subtract one from the other

Common mistakes

  • Using a guessed track-axis such as (1, 0, 1) and this must be the actual rest-position direction vector, not an approximation
  • Setting slave-name the same as target-name these must be different objects
  • Forgetting that track-axis depends on the rest geometry if you reposition objects in the 3D file you must recompute it
  • Note that the sign of track-axis does not matter, but the sign of lock-axis does.
  • Initial pose

    Initial pose

  • The target has moved and the locked-track animation ensures the object still points at the target (with the track-axis)

    The target has moved and the locked-track animation ensures the object still points at the target (with the track-axis)

  • The target is projected into the plane defined by the object center and the lock-axis before the locked-track animation is applied.

    The target is projected into the plane defined by the object center and the lock-axis before the locked-track animation is applied.

Slave center/object

The slave-center specifies the location of the middle revolute joint. The slave-name object (the lower arm) is automatically rotated around slave-center to follow the upper arm, so both arms always exactly fill the space between their two anchor points.

  • Initial pose

    Initial pose

  • The target has moved and the locked-track animation ensures the track-axis still points at the target. The object and the slave-object are rotated such that the available space is exactly filled (aka scissor animation).

    The target has moved and the locked-track animation ensures the track-axis still points at the target. The object and the slave-object are rotated such that the available space is exactly filled (aka scissor animation).

Examples

Basic locked-track (no slave)

Basic usage which is same behaviour as the Locked Track constraint in Blender. One object tracks a target point, rotating around the lock-axis: 

<?xml version="1.0" encoding="utf8"?>
<PropertyList>
  <animation>
    <type>locked-track</type>

    <object-name>ADS Arm - Fuselage.r</object-name>
    <center>
      <x-m>4.9</x-m>
      <y-m>1.47</y-m>
      <z-m>3.82</z-m>
    </center>
    <lock-axis>
      <x>0</x>
      <y>1</y>
      <z>0</z>
    </lock-axis>
    <track-axis>
      <x>0.75</x>
      <y>0</y>
      <z>-0.662</z>
    </track-axis>

    <target-name>ADS Arm - Ramp.r</target-name>
    <target-center>
      <x-m>7.969</x-m>
      <y-m>1.475</y-m>
      <z-m>1.11</z-m>
    </target-center>

  </animation>
</PropertyList>

Gear scissor in a single animation block

The standard scissors animation. One <animation> block drives both arms. object-name is the upper arm; slave-name is the lower arm. No parenting of objects in the 3D file is required. 

<?xml version="1.0" encoding="utf8"?>
<PropertyList>
  <animation>
    <type>locked-track</type>

    <object-name>ScissorsUpper</object-name>
    <center>
      <x-m>-4.00</x-m>   <!-- upper arm pivot on gear leg -->
      <y-m>0.10</y-m>
      <z-m>-1.20</z-m>
    </center>
    <lock-axis>
      <x>0</x>
      <y>1</y>           <!-- hinge pin runs left/right -->
      <z>0</z>
    </lock-axis>
    <track-axis>
      <x>0.19</x>        <!-- target-center minus center -->
      <y>0</y>
      <z>-0.23</z>
    </track-axis>

    <target-name>OleoStrut</target-name>
    <target-center>
      <x-m>-3.81</x-m>   <!-- lower arm pivot on oleo -->
      <y-m>0.10</y-m>
      <z-m>-1.43</z-m>
    </target-center>

    <slave-name>ScissorsLower</slave-name>
    <slave-center>
      <x-m>-3.90</x-m>   <!-- middle hinge where arms meet -->
      <y-m>0.10</y-m>
      <z-m>-1.31</z-m>
    </slave-center>
  </animation>
</PropertyList>

Disabling tracking with a condition

Use a condition to disable tracking and optionally apply a fixed rotation while disabled: 

<?xml version="1.0" encoding="utf8"?>
<PropertyList>
  <animation>
    <type>locked-track</type>

    <condition>
      <property>/controls/gear/nose-wheel-steering</property>
    </condition>
    <disabled-rotation-deg>-90</disabled-rotation-deg>

    <object-name>Torque Link Upper Arm</object-name>
    <center>
      <x-m>-9.785</x-m>
      <y-m>0</y-m>
      <z-m>1.04</z-m>
    </center>
    <lock-axis>
      <x>0</x>
      <y>1</y>
      <z>0</z>
    </lock-axis>
    <track-axis>
      <x>0.022</x>
      <y>0</y>
      <z>-1</z>
    </track-axis>

    <target-name>Torque Link Lower Arm</target-name>
    <target-center>
      <x-m>-9.789</x-m>
      <y-m>0</y-m>
      <z-m>0.454</z-m>
    </target-center>

    <slave-center>
      <x-m>-10.033</x-m>
      <y-m>0</y-m>
      <z-m>1.035</z-m>
    </slave-center>
  </animation>
</PropertyList>

Lessons learned

Scissors - with parenting

Scissors-locked-track-example.png

As seen to right, we have an oleo strut and a gear leg. The oleo strut has a compression animation which uses a translate animation to move up or down according to gear compression. There are two torque links, the top is called NLGTorqueLink1 and the bottom NLGTorqueLink2.

Note: parenting the bottom link to the top link in the 3D file is not required for the animation to work as the animation engine references objects by name only. The "with parenting" approach shown here is one valid modelling choice but is not mandatory, and may be problematic depending on the 3D file format being used (e.g. AC3D does not support poly objects with sub-objects).

After the translation animation, set up a locked-track animation on NLGTorqueLink1. The center is the hinge of the top scissor arm; target-name is the oleo strut which translates; slave-name is the bottom scissor arm; and slave-center is where the two arms meet. 

	<animation>
		<type>locked-track</type>
		<object-name>NLGTorqueLink1</object-name> <!-- upper -->
		<center>
		  <x-m>-13.468</x-m>
		  <y-m>-0.006419</y-m>
		  <z-m>-3.34389</z-m>
		</center>
		<lock-axis>
		  <x>0</x>
		  <y>-1</y> <!-- inverting lock-axis gives incorrect results -->
		  <z>0</z>
		</lock-axis>
		<track-axis> <!-- sign of track-axis does not matter -->
		  <x>0.100957</x>
		  <y>0.569667</y>
		  <z>0.001675</z>
		</track-axis>
		
		<target-name>NLGSlidingTubeAxle</target-name> <!-- oleo strut -->
		<target-center>  <!-- where lower arm attaches to oleo -->
		  <x-m>-13.569</x-m>
		  <y-m>-0.004744</y-m>
		  <z-m>-3.91356</z-m>
		</target-center>
		
		<slave-name>NLGTorqueLink2</slave-name>
		<slave-center>  <!-- middle hinge -->
		  <x-m>-13.2685</x-m>
		  <y-m>-0.005584</y-m>
		  <z-m>-3.67419</z-m>
		</slave-center>
	</animation>

Scissors - without parenting

The same animation can be done without any parenting in the 3D file, using two animation blocks where each arm tracks the other. Each torque link rotates around its base (where it meets the oleo strut or gear leg), locked on the Y-axis. Each arm's target-name is the other arm, target-center is the middle hinge point, and slave-center is the other arm's base pivot. 

	<animation>
		<type>locked-track</type>
		<object-name>NLGTorqueLink2</object-name> <!-- lower -->
		<center>
		  <x-m>-13.569</x-m>
		  <y-m>-0.004744</y-m>
		  <z-m>-3.91356</z-m>
		</center>
		<lock-axis>
		  <x>0</x>
		  <y>1</y>
		  <z>0</z>
		</lock-axis>
		<track-axis>
		  <x>0.100955</x>
		  <y>0.569668</y>
		  <z>0.001675</z>
		</track-axis>
		
		<target-name>NLGTorqueLink1</target-name>
		<target-center>  <!-- middle hinge -->
		  <x-m>-13.2685</x-m>
		  <y-m>-0.005584</y-m>
		  <z-m>-3.67419</z-m>
		</target-center>
		
		<slave-center> <!-- upper arm base pivot -->
		  <x-m>-13.468</x-m>
		  <y-m>-0.006419</y-m>
		  <z-m>-3.34389</z-m>
		</slave-center>
	</animation>
	
	<animation>
		<type>locked-track</type>
		<object-name>NLGTorqueLink1</object-name> <!-- upper -->
		<center>
		  <x-m>-13.468</x-m>
		  <y-m>-0.006419</y-m>
		  <z-m>-3.34389</z-m>
		</center>
		<lock-axis>
		  <x>0</x>
		  <y>1</y>
		  <z>0</z>
		</lock-axis>
		<track-axis>
		  <x>-0.100955</x>
		  <y>-0.569668</y>
		  <z>-0.001675</z>
		</track-axis>
		
		<target-name>NLGTorqueLink2</target-name>
		<target-center>  <!-- middle hinge -->
		  <x-m>-13.2685</x-m>
		  <y-m>-0.005584</y-m>
		  <z-m>-3.67419</z-m>
		</target-center>
		
		<slave-center> <!-- lower arm base pivot -->
		  <x-m>-13.569</x-m>
		  <y-m>-0.004744</y-m>
		  <z-m>-3.91356</z-m>
		</slave-center>
	</animation>

3 axis locked-track animation

Sometimes an object requires rotation in more than one plane which is often a hydraulic actuator with a ball joint. Since a single locked-track animation always needs at least one locked axis, this is handled by chaining two animations on the same object: one locking Y, immediately followed by one locking X, with all other parameters identical.

  • 3 axis locked-track animation example.

    3 axis locked-track animation example.

First, lock the Y axis and point the object at the target: 

    <animation>
        <type>locked-track</type>
        <object-name>gear-front-jack-02</object-name>
        <center>
            <x-m>-2.91953</x-m>
            <y-m>-0.06230</y-m>
            <z-m>-1.30829</z-m>
        </center>
        <lock-axis>
            <x>0</x>
            <y>1</y>
            <z>0</z>
        </lock-axis>
        <track-axis>
            <x>1</x>
            <y>-0.23</y>
            <z>0.630</z>
        </track-axis>
        <target-name>BOX_GEAR_GREEN.000</target-name>
        <target-center>
            <x-m>-2.04543</x-m>
            <y-m>-0.23232</y-m>
            <z-m>-0.82533</z-m>
        </target-center>
    </animation>

Immediately below it, add an identical block locking the X axis instead: 

    <animation>
        <type>locked-track</type>
        <object-name>gear-front-jack-02</object-name>
        <center>
            <x-m>-2.91953</x-m>
            <y-m>-0.06230</y-m>
            <z-m>-1.30829</z-m>
        </center>
        <lock-axis>
            <x>1</x>
            <y>0</y>
            <z>0</z>
        </lock-axis>
        <track-axis>
            <x>1</x>
            <y>-0.23</y>
            <z>0.630</z>
        </track-axis>
        <target-name>BOX_GEAR_GREEN.000</target-name>
        <target-center>
            <x-m>-2.04543</x-m>
            <y-m>-0.23232</y-m>
            <z-m>-0.82533</z-m>
        </target-center>
    </animation>

The track-axis

The track-axis is the direction the arm points in the rest position, i.e. the position the object occupies in the 3D file before any animation is applied. The correct value is simply: 

 track-axis = target-center - center

Read both points directly from vertex coordinates in your 3D application and subtract. Do not normalise the result. Do not guess a round value like (1, 0, 0) and even a small error here will cause the arm to start at the wrong angle.

Note that the coordinates use the plain <x>, <y>, <z> form (unitless direction vector), not the <x-m> form used for world-space positions.

Tips

AC3D users

The animation works by object name only and does not require any parent-child relationship between objects in the 3D file. If you are working with .ac files, do not attempt to nest a POLY inside another POLY to create parenting this violates the AC3D format and the editor will behave unpredictably. Simply name the objects correctly in the XML and the animation will work without any grouping in the file.

Using Blender

If you build your model in Blender you can verify the scissors animation before export by adding an armature with two bones, applying an IK constraint to the second bone tracking the target object, and attaching each scissor arm to its bone. The animation you see in Blender with this setup is exactly what the locked-track XML will produce in FlightGear.

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