Geometric Design of Independent Suspension Linkages

Abstract

The independent suspension allows each wheel of an automobile to move approximately vertically relative to the vehicle body without affecting the motion of the other wheels. Independent suspensions are designed when an existing vehicle is in need of improved performance or when an all-new vehicle is developed. The limitations of the modern suspension design approach are particularly apparent in the kinematics stage, where the linkage allowing the approximately-vertical wheel motion is selected and dimensioned. Selection is guided by experience, while dimensioning occurs by iterating a draft geometry. This is an expensive process, especially if the selected linkage is conceptually incapable of the desired motion. The desire to improve this kinematic design process resulted in four main contributions to the geometric design of independent suspension linkages.

The first contribution is the formulation of a mathematically-complete description of wheel motion. This description allows suspension designers to state a desired wheel trajectory before choosing any particular linkage, and to better understand the compromises inherent in stating the trajectory itself. The approach is to treat the wheel as a spatial rigid body, and place meaningful coordinates on SE(3), the group of spatial rigid body motions. These coordinates either are suspension characteristics of interest or may be easily mapped to such characteristics. A curve in SE(3) can then be defined based on the desired wheel kinematics, representing the desired wheel trajectory in a mathematically-coherent way.

The second contribution is a practical enumeration of spatial independent suspension linkages. This enumeration is systematic, generating potential linkage types from a set of practical body-wheel connections and basic assumptions on how these can be assembled into suspension linkages. The body-wheel connections considered are the revolute joint, spherical-spherical link, cylindrical joint, spherical joint, revolute-spherical link, revolute-revolute link, and spherical-cylindrical link. The underlying approach is extensible to other connection types and rules of construction. Such an enumeration is essential when wanting to consider all practical design possibilities.

The third contribution is dimensional synthesis methods for each of the considered body-wheel connections. These methods ensure each body-wheel connection can be dimensioned to its maximum practical capability. In general, these methods convert wheel position and/or velocity requirements into algebraic equations where the variables are the coordinates of the joint or link. This algebraic approach allows a large number of geometries to be generated rapidly. In general, the algebraic design equations are systems of polynomial equations, but, where possible, these are simplified into linear systems or closed form expressions.

The fourth contribution is a systematic approach for filtering and assembling individual connections into the enumerated linkages. Suspensions are required to satisfy application-specific non-kinematic design requirements, such as fitting within an allotted space or accommodating a steering system. The methods developed in this dissertation allow the numerous link solutions that achieve the kinematic requirements to be pruned and assembled into linkages according to these non-kinematic requirements, following a set-based design process.

Altogether, this dissertation presents a set of mathematical tools useful for specifying mathematically-complete wheel trajectories, enumerating possible suspension linkages, solving for linkage geometry, and satisfying non-kinematic requirements. Examples that demonstrate the efficacy of the methods are provided, including a complete synthesis example for each of the considered body-wheel connections. Examples include the semi-trailing arm, five link, double wishbone, control blade, and MacPherson strut architectures.