Mechanical and Computational Analysis of the Taylor Spatial Frame

Mechanical & Computational Analysis


of The

Taylor Spatial Frame



Ahmad R. Zamani

January 2017

  • An adaptation of parallel platforms (hexapod) for an orthopaedic frame (2002)

  • Manufacturer offers a web-based system for users

  • Instability reported despite all components remaining intact, which required avalysis of the configurations of the frame

Kinematics of TSF as a Hexapod

  • Can move and mobilise in all 6 degrees of freedom

  • Its Inverse Kinematics (IK) is simple while Forward Kinematics (FK) is challenging

  • Introduced in the 1950's and still being studied

  • Has many applications most widely for flight simulators


  • Solving the FK problem for hexapods in general

  • Having precise 3D models of the components

  • Visulalising the solutions in 3D on web

  • Addressing problems of variable geometries of body parts on which the frame is used

  • Modifying the geometries e.g. cutting the bone model


  • Scarcity of numerical tools in web platform like those available on workstations or desktops
  • 3D graphics on web is (still) a work in progress
  • Rapid pace of changes of web technologies at every level

How it was done?

  • Different numerical tools were tested and gaps were filled
  • Solution impletemted using both promising web 3D libraries were (x3d and threejs)
  • Other data visualisation tools (2D) were used and built on
  • Alternative solution for the FK problem developed using multibody dynamics
  • Implementation of entertainment (game) technologies for web were used


  • Web can be a very poweful research tool
  • A Kinematic problem cam be solved by a fully dynamic multibody simulation
  • Accurate 3D visualisation can be a tool to enhance precision in corrective surgeries in orthopaedics e.g. via preplanning

TSF Rings

  • The name "ring fixator" is given to these type of orthopaedic devices
  • Their behaviour is important as the support of the pins and wires
  • Their mechanics is not well studied especially compared to the wires
  • In their simple form, the rings in orthopaedic fixators can be considered as thick curved castellated beams

Please check:


  • The mechanics of thick castellated curved beams does not have a theoretical solution
  • TSF rings are mostly made as two half-rings attached by one (or two pairs) of bolts, therefore need to be modelled in 3D
  • They have fillets which requires accurate geometric modelling in 3D using a computational method like Finite Elements (FE)
  • They have a varitey of sizes ans shapes, i.e. half-rings, fuu rings, 2/3 rings and from under 100 mm to 230 mm in diameter


  • The availability of less common ring shapes and sizes
  • FE modelling of the tests which were performed with minimal intervention to reveal the nature of the rings behavoiur
  • FE modelling of the boundary conditions not to impose unnecessary idealisation

How it was done? (I)

  • TSF ring were provided for testing by Dr. Michalis Zenios
  • The TSF rings were tested under in-plane compression in the school of MACE workshop (by Mr. David Mortimer)
  • Tests werer simulated using Abaqus software package
  • Pieces of the materials were machined out and tested for material property (by Mr. Peter Hassall)
  • Full range of elasto-plastic material behaviour were integrated in the FE models

How it was done? (II)

  • Models were validated by results from the mechanical tests
  • Scripts were written for automated generation of geometry, meshing and analysis of different possible loadingd alog all ring diameters


  • Rings made with two half-rings are less-stiff and less well-bahaved, i.e. using bolts to attach half-rings is a source of weakness
  • Larger rings are weaker despite the fact that they need to be stronger
  • Stifness varies with the loading axis, the wire clamps on the ring affects its stiffness

Thanks for your attention