Accelerations in the Ball Joint

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A procedure for calculating relative accelerations in spatial mechanisms is extended to include ball joints. The relationship of the relative velocities in a closed-loop mechanism is differentiated and then manipulated into set of simultaneous linear equations in the unknown relative accelerations. The derivatives of the joint-link modeling matrices, which are required to construct the vector of constants in this set of simultaneous linear equations, are formulated in terms of partial-derivative operator matrices to facilitate automatic differentiation in computer calculations. The joint-link modeling matrices, the relative velocities, and the relative accelerations are written in terms of dual numbers so to provide compact expressions which can be readily coded in object-oriented programming. The relationship of the calculated relative-acceleration components, which are expressed in the same coordinate frame, and the physical relative-acceleration components, which are naturally expressed in different coordinate frames, is developed and explained. The RSSR spatial four-bar mechanism is presented as an example of the methodology applied to a mechanism with ball joints.

Original languageEnglish (US)
Pages (from-to)1-16
Number of pages16
JournalMechanics Based Design of Structures and Machines
Issue number1
StatePublished - Jan 2 2014

All Science Journal Classification (ASJC) codes

  • Civil and Structural Engineering
  • General Mathematics
  • Automotive Engineering
  • Aerospace Engineering
  • Condensed Matter Physics
  • Ocean Engineering
  • Mechanics of Materials
  • Mechanical Engineering


  • Acceleration
  • Ball joint
  • Dual number
  • RSSR
  • Relative acceleration


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