A vehicle on elastic suspensions may be modelled as a system made by a certain number of rigid bodies connected with each other by mechanisms of various kinds and by a set of massless springs and dampers simulating the suspensions. A vehicle with four wheels can be modelled as a system with 10 degrees of freedom, six for the body and one for each wheel. This holds for any type of suspension, if the motion of the wheels due to the compliance of the system constraining the motion of the suspensions (longitudinal and transversal compliance of the suspensions) is neglected | 29 MULTIBODY MODELLING A vehicle on elastic suspensions may be modelled as a system made by a certain number of rigid bodies connected with each other by mechanisms of various kinds and by a set of massless springs and dampers simulating the suspensions. A vehicle with four wheels can be modelled as a system with 10 degrees of freedom six for the body and one for each wheel. This holds for any type of suspension if the motion of the wheels due to the compliance of the system constraining the motion of the suspensions longitudinal and transversal compliance of the suspensions is neglected. The wheels of each axle may be suspended separately independent suspensions or together solid axle suspensions but the total number of degrees of freedom is the same Fig. . Additional degrees of freedom such as the rotation of the wheels about their axis or about the kingpin can be inserted into the model to allow the longitudinal slip or the compliance of the steering system to be taken into account. The multibody approach can be pushed much further by modelling for instance each of the links of the suspensions as a rigid body. To model a short-long arms SLA suspension it is possible to resort to three rigid bodies simulating the lower and upper triangles and the strut plus a further rigid body simulating the steering bar. While modelling the system in greater detail the number of rigid bodies included in the model increases. However if the compliance of the various elements is neglected . if these bodies are rigid bodies the number of degrees of freedom does not increase along with the number of bodies an SLA suspension always has a single degree of freedom even if it is made up of a number of rigid bodies simulating its various elements. The mathematical model of a multibody system is thus made up of the equations of motion of the various elements which in tri-dimensional space are 6n if n is the number of the rigid bodies plus a suitable number of constraint equations.
