Inverse dynamics of a 3-PRC parallel kinematic machine

Yangmin Li, Stefan Staicu

Research output: Journal article publicationJournal articleAcademic researchpeer-review

56 Citations (Scopus)


Recursive matrix relations for kinematics and dynamics analysis of a three-prismatic-revolute-cylindrical (3-PRC) parallel kinematic machine (PKM) are performed in this paper. Knowing the translational motion of the platform, we develop first the inverse kinematical problem and determine the positions, velocities and accelerations of the robot's elements. Further, the inverse dynamic problem is solved using an approach based on the principle of virtual work and the results in the framework of the Lagrange equations with their multipliers can be verified. Finally, compact matrix equations and graphs of simulation for input force and power of each of three actuators are obtained. The investigation of the dynamics of this parallel mechanism is made mainly to solve successfully the control of the motion of such robotic system.
Original languageEnglish
Pages (from-to)1031-1041
Number of pages11
JournalNonlinear Dynamics
Issue number2
Publication statusPublished - 1 Jan 2012
Externally publishedYes


  • Dynamics modelling
  • Kinematics
  • Lagrange equations
  • Parallel kinematic machine
  • Virtual work

ASJC Scopus subject areas

  • Applied Mathematics
  • Mechanical Engineering
  • Aerospace Engineering
  • Ocean Engineering
  • Electrical and Electronic Engineering
  • Control and Systems Engineering


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