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The paper presents a vector algebraic method for the displacement and force analysis of the five-rod wheel suspension mechanism, used as a rear suspension in some modern cars. Displacement equations are derived by using the solutions of the vector tetrahedron equations obtained as the closure or constraint equations for spatial multi-loop mechanisms. The method gives the possibility of reducing the system of constraint equations from the original five to two. The resultant equations are expressed in recursive notation, which isrelatively concise in form and convenient for programming, providing a very efficient and accurate algorithm. The system of force and torque equilibrium equations is solved in an explicit way. Flexible joints with experimentally determined linearized compliance matrices are taken into consideration, leading to an algorithm for elastokinematic analysis of the mechanism. Graphical illustration of the results is also presented.

The paper describes a novel algorithm for solving the synthesis problem of a multi-link wheel-guiding mechanism with a known topology and dimension. The synthesis objectives contain the elastokinematical specifications, described by a set of spatial displacements that the wheel carrier should undergo from a design position under specified loads corresponding to typical car manoeuvres. Radial spring rates of cylindrical elastomeric bushings, embodied in the suspension rods, are considered as design variables. Relations between the design variables and the objectives are established using the first-order kinematics and screw calculus, under assumptions about small displacements and linear force-deflection characteristics of the flexible elements. The problem is solved by using a constrained linear least-squares algorithm. Depending whether the input data is provided by a designer or acquired during suitable experiments, the algorithm can be used for synthesis or estimation of the stiffness parameters. Numerical examples are solved for two five-rod suspensions, with the same topology but different configuration and dimension, installed at rear-driven axles of actual cars. Static spring rates of the five rod-bushings are determined, for which both suspensions satisfy the formulated ride/handling criteria in the best way. Fundamental characteristics and limitations of the suspensions are described.

Position and displacement analysis of a spherical model of a human knee joint using the vector method was presented. Sensitivity analysis and parameter estimation were performed using the evolutionary algorithm method. Computer simulations for the mechanism with estimated parameters proved the effectiveness of the prepared software. The method itself can be useful when solving problems concerning the displacement and loads analysis in the knee joint.

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