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<article data-uid="Usage.HiMech.Topo">
<h1 id="kinematic-topology">Kinematic Topology</h1>
<p>The Kinematic Topology is composed of three elemental classes: <strong><a class="xref" href="../../../../../api/Hi.Mech.Topo.Anchor.html">Anchor</a></strong>, <strong><a class="xref" href="../../../../../api/Hi.Mech.Topo.Branch.html">Branch</a></strong> and <strong><a class="xref" href="../../../../../api/Hi.Mech.Topo.Asmb.html">Asmb</a></strong>.</p>
<h2 id="basic-elements">Basic Elements</h2>
<h3 id="anchors-and-branches">Anchors and Branches</h3>
<p><strong><a class="xref" href="../../../../../api/Hi.Mech.Topo.Anchor.html">Anchor</a></strong> object contains a cartesian coordinate. It can be a mechanical component or a flag.</p>
<p><strong><a class="xref" href="../../../../../api/Hi.Mech.Topo.Branch.html">Branch</a></strong> object is a directional link between two <a class="xref" href="../../../../../api/Hi.Mech.Topo.Anchor.html">Anchor</a> objects. It contains the <strong><a class="xref" href="../../../../../api/Hi.Mech.Topo.ITransformer.html">ITransformer</a></strong> object. The <a class="xref" href="../../../../../api/Hi.Mech.Topo.ITransformer.html">ITransformer</a> object contains a coordinate <strong>transformation matrix</strong>. As shown in the following sketch:</p>
<p><img src="chainLink.png" alt="Chain Structure"></p>
<h3 id="assembly-management">Assembly Management</h3>
<p><strong><a class="xref" href="../../../../../api/Hi.Mech.Topo.Asmb.html">Asmb</a></strong> (Assembly) provides organization and management of Anchors. An Assembly can contain both Anchors and other Assemblies. Key features include:</p>
<ul>
<li>Grouping related Anchors together</li>
<li>Managing coordinate transformations</li>
<li>Providing display and indexing functions</li>
<li>Supporting hierarchical structure</li>
</ul>
<h2 id="kinematic-chain-example">Kinematic Chain Example</h2>
<p>The following figure shows a kinematic chain of a non-orthogonal 5-axis machine tool:</p>
<p><img src="vmt.png" alt="VMT Structure"></p>
<p>Each <a class="xref" href="../../../../../api/Hi.Mech.Topo.Anchor.html">Anchor</a> represents a component:</p>
<ul>
<li>Axis components: X, Y, Z, B, C</li>
<li>Base components: O (base1), O* (base2)</li>
<li>Tool components: S (spindle), T (tool body), T* (tool flute)</li>
<li>Workpiece: W</li>
</ul>
<p>The relative transform between two Anchors is calculated by multiplying the transform matrices along the Branch. For example, the transform matrix from W to T is:</p>
<div class="math">
\[
M_{WT} = M_{CW}^{-1} \cdot M_{YC}^{-1} \cdot M_{OY}^{-1} \cdot M_{OO^*} \cdot M_{O^*X} \cdot M_{XZ} \cdot M_{ZB} \cdot M_{BS} \cdot M_{ST}
\]</div>
<p>This matrix can be obtained using <a class="xref" href="../../../../../api/Hi.Mech.Topo.Asmb.html#Hi_Mech_Topo_Asmb_GetMat4d_Hi_Mech_Topo_IGetAnchor_Hi_Mech_Topo_IGetAnchor_">GetMat4d(IGetAnchor, IGetAnchor)</a>.</p>
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<article data-uid="HiMech.Overview">
<h1 id="mechanism-topology">Mechanism Topology</h1>
<p>HiAPI Mechanism Topology provides basic functionality for assembling mechanical structures and simulating their motions. It allows you to build kinematic models of milling machines and similar mechanical structures through a topology-based approach.</p>
<h2 id="core-concepts">Core Concepts</h2>
<h3 id="kinematic-topology">Kinematic Topology</h3>
<p>Kinematic Topology is the core concept of this module, which describes the motion relationships between mechanical components. With Kinematic Topology, you can:</p>
<ul>
<li>Define mechanical structures and motion relationships</li>
<li>Calculate forward and inverse kinematics</li>
<li>Display component positions and orientations</li>
<li>Conduct collision detection</li>
</ul>
<h3 id="main-modules">Main Modules</h3>
<ul>
<li><a href="Topo/index.html">Topology</a> - Kinematic topology structure, including assembly management and chain definition</li>
<li><a href="transformers/index.html">Transformers</a> - Coordinate transformation and motion transformation</li>
</ul>
<h2 id="api-references">API References</h2>
<ul>
<li><a class="xref" href="../../../../api/Hi.Mech.Topo.html">Hi.Mech.Topo</a> - Core topology functionality</li>
<li><a class="xref" href="../../../../api/Hi.Mech.Topo.Asmb.html">Asmb</a> - Assembly-related functionality</li>
<li><a class="xref" href="../../../../api/Hi.Mech.Topo.Branch.html">Branch</a> - Chain-related functionality</li>
</ul>
<h2 id="examples">Examples</h2>
<p>Please refer to the examples in each sub-section to learn how to use these features to build your applications.</p>
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<article data-uid="HiMech.Tutor.transformers">
<h1 id="handle-transform-matrix-by-itransformer">Handle Transform Matrix by ITransformer</h1>
<p><strong><a class="xref" href="../../../../../api/Hi.Mech.Topo.ITransformer.html">ITransformer</a></strong> contains a transform matrix and a inverse transform matrix. The matrix is 4x4 column-major matrix, which describe the orientation or movement between 3D coordinates.</p>
<p>Several common used interface and class are implemented from <a class="xref" href="../../../../../api/Hi.Mech.Topo.ITransformer.html">ITransformer</a>. The inheritance is shown:</p>
<ul>
<li><a class="xref" href="../../../../../api/Hi.Mech.Topo.IStaticTransformer.html">IStaticTransformer</a>
<ul>
<li><a class="xref" href="../../../../../api/Hi.Mech.Topo.NoTransform.html">NoTransform</a></li>
<li><a class="xref" href="../../../../../api/Hi.Mech.Topo.StaticTranslation.html">StaticTranslation</a></li>
<li><a class="xref" href="../../../../../api/Hi.Mech.Topo.StaticRotation.html">StaticRotation</a></li>
<li><a class="xref" href="../../../../../api/Hi.Mech.Topo.StaticFreeform.html">StaticFreeform</a></li>
</ul>
</li>
<li><a class="xref" href="../../../../../api/Hi.Mech.Topo.IDynamicTransformer.html">IDynamicTransformer</a>
<ul>
<li><a class="xref" href="../../../../../api/Hi.Mech.Topo.IDynamicRegular.html">IDynamicRegular</a>
<ul>
<li><a class="xref" href="../../../../../api/Hi.Mech.Topo.DynamicTranslation.html">DynamicTranslation</a></li>
<li><a class="xref" href="../../../../../api/Hi.Mech.Topo.DynamicRotation.html">DynamicRotation</a></li>
</ul>
</li>
<li><a class="xref" href="../../../../../api/Hi.Mech.Topo.DynamicFreeform.html">DynamicFreeform</a></li>
</ul>
</li>
</ul>
<p><strong><a class="xref" href="../../../../../api/Hi.Mech.Topo.IStaticTransformer.html">IStaticTransformer</a></strong> is transformer with constant matrix. <strong><a class="xref" href="../../../../../api/Hi.Mech.Topo.NoTransform.html">NoTransform</a></strong>, <strong><a class="xref" href="../../../../../api/Hi.Mech.Topo.StaticTranslation.html">StaticTranslation</a></strong> and <strong><a class="xref" href="../../../../../api/Hi.Mech.Topo.StaticRotation.html">StaticRotation</a></strong> contains transform matrix of identity, translate and rotate respectively. <strong><a class="xref" href="../../../../../api/Hi.Mech.Topo.StaticFreeform.html">StaticFreeform</a></strong> contains a arbitrary constant transform matrix.</p>
<p>The transform matrix of <a class="xref" href="../../../../../api/Hi.Mech.Topo.StaticTranslation.html">StaticTranslation</a> is:</p>
<div class="math">
\[
M_{StaticTranslate}=
\begin{bmatrix}
1 &amp; 0 &amp; 0 &amp; 0 \\\\
0 &amp; 1 &amp; 0 &amp; 0 \\\\
0 &amp; 0 &amp; 1 &amp; 0 \\\\
Trans.x &amp; Trans.y &amp; Trans.z &amp; 1
\end{bmatrix}
\]</div>
<p>The transform matrix of <a class="xref" href="../../../../../api/Hi.Mech.Topo.StaticRotation.html">StaticRotation</a> and <a class="xref" href="../../../../../api/Hi.Mech.Topo.DynamicRotation.html">DynamicRotation</a> is:</p>
<div class="math">
\[
M_{Rotate}=
\begin{bmatrix}
1 &amp; 0 &amp; 0 &amp; 0 \\\\
0 &amp; 1 &amp; 0 &amp; 0 \\\\
0 &amp; 0 &amp; 1 &amp; 0 \\\\
-Pivot.x &amp; -Pivot.y &amp; -Pivot.z &amp; 1
\end{bmatrix}
\cdot
\\\\
\begin{bmatrix}
Rot_{00}(axis,rad) &amp; Rot_{01}(axis,rad) &amp; Rot_{02}(axis,rad) &amp; 0 \\\\
Rot_{10}(axis,rad) &amp; Rot_{11}(axis,rad) &amp; Rot_{12}(axis,rad) &amp; 0 \\\\
Rot_{20}(axis,rad) &amp; Rot_{21}(axis,rad) &amp; Rot_{22}(axis,rad) &amp; 0 \\\\
0 &amp; 0 &amp; 0 &amp; 1
\end{bmatrix}
\cdot
\\\\
\begin{bmatrix}
1 &amp; 0 &amp; 0 &amp; 0 \\\\
0 &amp; 1 &amp; 0 &amp; 0 \\\\
0 &amp; 0 &amp; 1 &amp; 0 \\\\
Pivot.x &amp; Pivot.y &amp; Pivot.z &amp; 1
\end{bmatrix}
\]</div>
<p>Where <a class="xref" href="../../../../../api/Hi.Mech.Topo.DynamicRotation.html#Hi_Mech_Topo_DynamicRotation_Pivot">Pivot</a> is the position of the rotation axis.</p>
<div class="TIP">
<h5>Tip</h5>
<p>Pivot is a point. However, rotation axis is a line. It means that it causes the same matrix no matter how the pivot is moving along the axis.</p>
</div>
<p><strong><a class="xref" href="../../../../../api/Hi.Mech.Topo.IDynamicTransformer.html">IDynamicTransformer</a></strong> is transformer with inconstant transform matrix. <strong><a class="xref" href="../../../../../api/Hi.Mech.Topo.IDynamicRegular.html">IDynamicRegular</a></strong> has a property <a class="xref" href="../../../../../api/Hi.Mech.Topo.IDynamicRegular.html#Hi_Mech_Topo_IDynamicRegular_Step">Step</a>, implied that the transform matrix is one parameter driven. <a class="xref" href="../../../../../api/Hi.Mech.Topo.TransformerUtil.html#Hi_Mech_Topo_TransformerUtil_GetSteps_Hi_Mech_Topo_IDynamicRegular___">GetSteps(IDynamicRegular[])</a> and <a class="xref" href="../../../../../api/Hi.Mech.Topo.TransformerUtil.html#Hi_Mech_Topo_TransformerUtil_SetSteps_Hi_Mech_Topo_IDynamicRegular___System_Double___">SetSteps(IDynamicRegular[], double[])</a> provide easy handle of an array of <a class="xref" href="../../../../../api/Hi.Mech.Topo.IDynamicRegular.html">IDynamicRegular</a> objects.</p>
<p>The transform matrix of <a class="xref" href="../../../../../api/Hi.Mech.Topo.DynamicTranslation.html">DynamicTranslation</a> is:</p>
<div class="math">
\[
M_{DynamicTranslate}=
\begin{bmatrix}
1 &amp; 0 &amp; 0 &amp; 0 \\\\
0 &amp; 1 &amp; 0 &amp; 0 \\\\
0 &amp; 0 &amp; 1 &amp; 0 \\\\
Trans.x \cdot Step &amp; Trans.y \cdot Step &amp; Trans.z \cdot Step &amp; 1
\end{bmatrix}
\]</div>
<div class="NOTE">
<h5>Note</h5>
<p>In convention, <a class="xref" href="../../../../../api/Hi.Mech.Topo.StaticTranslation.html#Hi_Mech_Topo_StaticTranslation_Trans">Trans</a> should be normalized.</p>
</div>
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