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KSME International Journal

, Volume 18, Issue 4, pp 550–559 | Cite as

A recursive algorithm for generating the equations of motion of spatial mechanical systems with application to the five-point suspension

  • Hazem Ali Attia
Article

Abstract

In this paper, a recursive formulation for generating the equations of motion of spatial mechanical systems is presented. The rigid bodies are replaced by a dynamically equivalent constrained system of particles which avoids introducing any rotational coordinates. For the open-chain system, the equations of motion are generated recursively along the serial chains using the concepts of linear and angular momenta. Closed-chain systems are transformed to open-chain systems by cutting suitable kinematic joints and introducing cut-joint constraints. The formulation is used to carry out the dynamic analysis of multi-link five-point suspension. The results of the simulation demonstrate the generality and simplicity of the proposed dynamic formulation.

Key Words

Multibody System Dynamics Equations of Motion System of Rigid Bodies Mechanisms Machine Theory 

Nomenclature

di,j

Distance between pointsi andj

G1

Vector sum of the moments of the external forces and force couples acting on the body with respect to particle 1

Iξξ,Iηη,Iζζ

Moments of inertia of the body with respect to the body attached coordinate frame

Iξη,Iξζ,Iζη

Products of inertia of the body with respect to the body attached coordinate frame

m

Mass of the body

mi

Mass of particlei

mi,j

Mass of the secondary particle that is located between the primary particlesi andj

\(\bar r_G \)

The position vector of the centre of mass of the body with respect to the body attached coordinate frame

\(\bar r_i \)

Position vector of particle i with respect to the body attached coordinate frame

\(r_i ,\dot r,\ddot r_i \)

Position, velocity, and acceleration vectors of particle i with respect to an inertial reference frame

\(r_{i,j} ,\dot r_{i,j} ,\ddot r_{i,j} \)

Relative position, velocity, and acceleration vectors between particlesi andj

riTrj

Algebraic notation denotes the dot product operation (ri,r)

\(\tilde r_i r_j \)

Algebraic notation denotes the cross product operation (rixrj)

R

Vector sum of the external forces acting on the rigid body

ξi, ηi, ζi

Coordinates of particle i with respect to the body attached coordinate frame

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References

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Copyright information

© The Korean Society of Mechanical Engineers (KSME) 2004

Authors and Affiliations

  1. 1.Department of Mathematics, College of ScienceKing Saud University, (Al-Qasseem Branch)BuraidahKSA

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