KSME International Journal

, Volume 18, Issue 4, pp 550–559

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

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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