Jacobian approach to the kinestatic analysis of a full vehicle model with application to cornering motion analysis

Abstract

The Jacobian approach to the kinestatic analysis of a planar suspension mechanism has been previously presented. In this paper, the theory is extended to three-dimensional kinestatic analysis by developing a full kinematic model and viewing it as a spatial parallel mechanism. The full kinematic model consists of two pairs of the front (double wishbone) and rear (multi-link) suspension mechanisms together with a newly developed ground-wheel contact model. The motion of each wheel of four suspension mechanisms is represented by the corresponding instantaneous screw at any instant. A vehicle is considered to be a 6-degrees-of-freedom spatial parallel mechanism whose vehicle body is supported by four serial kinematic chains. Each kinematic chain consists of a virtual instantaneous screw joint and a kinematic pair representing ground-wheel contact model. The kinestatic equation of the 6-degrees-of-freedom spatial parallel mechanism is derived in terms of the Jacobian. As an important application, a cornering motion of a vehicle is analysed under the assumption of steady-state cornering. A numerical example is presented to illustrate how to determine the optimal locations of strut springs for the least roll angle in cornering motion using the proposed method.

Keywords

Jacobian kinestatic analysis steady-state cornering full vehicle model reciprocal Jacobian theory of screws

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References

Dixon

. The roll-centre concept in vehicle handling dynamics. Proc IMechE, Part D: J Automobile Engineering 1987; 201: 69–78.

Morse P and Starkey JM. A force-based roll centre model for vehicle suspensions. SAE Paper 962536, 1996.

Mitchell WC. Asymmetric roll centres. SAE Paper 983085, 1998.

Moline D, Vaduri S and Law EH. Fidelity of vehicle models using roll centre principles. SAE Paper 2000-01-0693, 2000.

Lee

Shim

. Roll center analysis of a half-car model using pole for small displacement. Int J Automot Technol 2006; 7: 833–839.

Kim

Hong

Choi

. New Jacobian approach to the kinestatic analysis of a planar double-wishbone suspension mechanism. Proc IMechE, Part D: J Automobile Engineering 2013; 227: 1085–1096.

Suh CH. Suspension analysis with instant screw axis theory. SAE Paper 910017, 1991.

Lee

Han

. A method for predicting dynamic behaviour characteristics of a vehicle using the screw theory – part 1. Proc IMechE, Part D: J Automobile Engineering 2008; 222: 65–77.

Lee JK. Applications of screw axis theory to the behavior analysis of full-vehicle models and the synthesis of suspension system. PhD Thesis, Korea University, Korea, 2007.

10.

Duffy

. Statics and kinematics with applications to robotics, New York: Cambridge University Press, 1996.

11.

Hong MB. Reciprocal Jacobian approach to kinestatic analysis of robots and passive compliance realization. PhD Thesis, Yonsei University, Korea, 2009.

12.

Tsai

. Robot analysis: the mechanics of serial and parallel manipulators, New York: John Wiley, 1999.

13.

Gillespie

. Fundamentals of vehicle dynamics, Warrendale: Society of Automotive Engineers, 1992.

14.

Bian M, Chen L, Luo Y, et al. A dynamic model for tyre/road friction estimation under combined longitudinal/lateral slip situation. SAE Tech Paper Series No. 2014-01-0123, 2014.

15.

Dixon

. Tires, suspension and handling, 2th ed. Warrendale: Society of Automotive Engineers, 1996.

16.

Guiggiani

. The science of vehicle dynamics, 2th ed. Dordrecht: Springer, 2018.