The Study Of Dynamic Simulation Of Macpherson Suspension Based On The Natural Coordinate Method

The dynamics of multibody systems is a new subject which based on the classic mechanics. It is proper used in the engineering project that is including many bodies with unlimited movement. With the development of computer science, it makes it possible to calculate the complex system accurately in a large scale by the combination of multibody system dynamics and computer science.The dynamics of multibody systems is a kind of high-efficiency and high-precision analytical approach, and has obtained tremendous advances in about twenty years. It defines the method of the dynamics of multibody system in two different ways according to the different coordinates. They are absolute coordinate method which is also called Cartesian method and relative coordinate method which is also called Lagrange method. In 1990s, Garclde Jalon and Bayo produced the natural coordinate method, and brought out some monographs. The natural coordinate method is another kind of Cartesian coordinate method. And it uses the Cartesian coordinates of the reference point and reference vector that are consolidated to the rigid body to describe its spatial position and pose, and need not use the Eulerian angles and Euler parameters. Usually, the reference point selects the centre of joint,and the reference vector follows the rotational axis or slip axis of joint. the reference point or vector is usually shared by several rigid body ,so lead the number of unknown variates decrease. All of the constraint equations arequadric algebraic equation of coordinates, and the Jacobian matrices are linear function of coordinates. Thus lead the computing time prominently decrease. But it is a little random to build the constraint equation with natural coordinate method, so it is not prone to compile the universal simulated program. This disquisition introduced the natural coordinate four-point method which based on the natural coordinate method to solve the problem. Except for the excellency of the natural coordinate method ,the generation type of constraint equation and kinetic equation are fixed,so it is easier to compile the universal simulated program.The definition of this method is: select four points c , p1 , p2 ,p3 on rigid body, and define the vectors cp 1 , cp 2,cp 3 are unit vectors, so they can form a right hand Cartesian coordinate system whose origin is the point c , and keep this coordinate system act as the link-body basement of the rigid body. Then we can analyze the position and pose of the rigid body in inertial system.This disquisition has completed following development work based on the natural coordinate four-point method:1. Detailedly introduced the position and pose of rigid body in inertial system.2. Deduced the expressions of the position,velocity,acceleration of a random point on rigid body as well as the formulate of the angular velocity and angular acceleration of rigid body3. Detailedly introduced the constrain equations of the spherical joint,universal joint,revolute joint,cylindrical joint and translational joint.4. Use the natural coordinate four-point method and D'Alembert's principle to analyze the dynamic problem of a spatial random rigid body and two spatial rigid bodies which are reciprocal bond.5. Use the natural coordinate four-point method and the Matlab software to simulate the kinematic and dynamic characteristic of theMacpherson suspension, and then compare the simulated results with which have been done in ADAMS software, they almost completely dovetail. So it proved the method is correct.