Table of Contents

Kinematic Topology

The Kinematic Topology is composed of three elemental classes: Anchor, Branch and Asmb.

Basic Elements

Anchors and Branches

Anchor object contains a cartesian coordinate. It can be a mechanical component or a flag.

Branch object is a directional link between two Anchor objects. It contains the ITransformer object. The ITransformer object contains a coordinate transformation matrix. As shown in the following sketch:

Chain Structure

Assembly Management

Asmb (Assembly) provides organization and management of Anchors. An Assembly can contain both Anchors and other Assemblies. Key features include:

  • Grouping related Anchors together
  • Managing coordinate transformations
  • Providing display and indexing functions
  • Supporting hierarchical structure

Kinematic Chain Example

The following figure shows a kinematic chain of a non-orthogonal 5-axis machine tool:

VMT Structure

Each Anchor represents a component:

  • Axis components: X, Y, Z, B, C
  • Base components: O (base1), O* (base2)
  • Tool components: S (spindle), T (tool body), T* (tool flute)
  • Workpiece: W

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:

\[ M_{WT} = M_{CW}^{-1} \cdot M_{YC}^{-1} \cdot M_{OY}^{-1} \cdot M_{OO^*} \cdot M_{O^*X} \cdot M_{XZ} \cdot M_{ZB} \cdot M_{BS} \cdot M_{ST} \]

This matrix can be obtained using GetMat4d(IGetAnchor, IGetAnchor).