International Journal of Automotive Technology

, Volume 20, Issue 1, pp 137–145

# Application of Screw Theory to the Analysis of Instant Screw Axis of Vehicle Suspension System

• Jae Kil Lee
• Jae Kyung Shim
Article

## Abstract

This paper proposes a method using screw theory to find the twist of a rigid body of a mechanism. For this, a geometric method to determine the screws and reciprocal screws associated with kinematic joints and links is introduced. This geometric method provides a simple way to find the wrenches acting upon a rigid body of a mechanism using the joint types and positions. Then, the twist which is reciprocal to the wrenches is determined to find the instant screw axis and pitch of the body. The proposed method is applied to planar mechanisms and spatial suspension mechanisms. For planar mechanisms, the method finds the instant center of velocity as the point in the plane of planar motion intersected by the instant screw axis. Using the proposed method, the instant screw axes and pitches are determined for the bump-rebound motion and steering motion of the double wishbone, McPherson strut, and 5-SS multi-link type suspension mechanisms. The numerical results agree with findings of previous researches.

## Key words

Suspension mechanism Kinematic analysis Screw theory Instant screw axis Steering axis

## References

1. An, H. S., Lee, J. H., Lee, C., Seo, T. and Lee, J. W. (2017). Geometrical kinematic solution of serial spatial manipulators using screw theory. Mechanism and Machine Theory, 116, 404–418.
2. Ball, R. S. (1900). A Treatise on the Theory of Screws. Cambridge University Press. New York, USA.
3. Choi, J. S. (2000). Approximate Synthesis of 5-SS Multilink Suspension and Analysis of Instantaneous Screw Axis Using Line Geometry. M. S. Thesis. Korea University. Seoul, Korea.Google Scholar
4. Choi, J. S. and Shim, J. K. (2000). Analysis of instantaneous screw axis of a 5-ss multi-link suspension system using line geometry. Proc. KSME Fall Annual Meeting, 635–640.Google Scholar
5. Davidson, J. K. and Hunt, K. H. (2004). Robots and Screw Theory: Applications of Kinematics and Statics to Robotics. Oxford University Press. New York, USA.
6. Gibson, C. G. and Hunt, K. H. (1990). Geometry of screw systems-2: Classification of screw systems. Mechanism and Machine Theory 25, 1, 11–27.
7. Huang, Z., Li, Q. and Ding, H. (2013). Theory of Parallel Mechanisms. Springer. Dordrecht, The Netherlands.
8. Hunt, K. H. (1978). Kinematic Geometry of Mechanisms. Clarendon Press. Oxford, UK.
9. Kim, S. P. (1999). Approximate Synthesis of Multi-link Type Suspension Systems Using Instantaneous Screw Axis. Ph. D. Dissertation. Korea University. Seoul, Korea.Google Scholar
10. Kim, S. P., Shim, J. K., Lee, U. K. and Ahn, B. E. (2001). Approximate synthesis of a multi-link type suspension with steering. Trans. Korean Society of Mechanical Engineers A 25, 1, 32–38.Google Scholar
11. Kim, S. S. and Kim, S. H. (2014). Steering axis analysis of multi-link suspensions with bushing compliance. Trans. Korean Society of Automotive Engineers 22, 3, 194–202.
12. Lee, J. K. and Shim, J. K. (2006). Roll center analysis of a half-car model using pole for small displacement. Int. J. Automotive Technology, 7, 7, 833–839.Google Scholar
13. Lee, J. K. and Shim, J. K. (2011). Validity and limitations of the kinematic roll center concept in the viewpoint of spatial kinematics using screw theory. Int. J. Automotive Technology 12, 5, 769–775.
14. Lee, J. M. (1996). Analysis of Instantaneous Screw Axis in Multi-link Suspension System and Its Application to Sensitivity Analysis. M. S. Thesis. Korea University. Seoul, Korea.Google Scholar
15. Lee, U. and Ahn, B. (1993). A method to analyze “the imaginary kingpin axis” in multi-link type suspension system. SAE Paper No. 930262.Google Scholar
16. Reddy, K., Kodati, M., Chatra, K. and Bandyopadhyay, S. (2016). A comprehensive kinematic analysis of the double wishbone and MacPherson strut suspension systems. Mechanism and Machine Theory, 105, 441–470.
17. Roth, B. (1984). Screws, motors, and wrenches that cannot be bought in a hardware store. Proc. 1st Int. Symp. Robotics Research, 679–693.Google Scholar
18. Suh, C. H. (1991). Suspension analysis with instant screw axis theory. SAE Paper No. 910017.Google Scholar
19. Tsai, L. W. (1999). Robot Analysis: The Mechanics of Serial and Parallel Manipulators. John Wiley & Sons. New York, USA.Google Scholar
20. Woo, L. and Freudenstein, F. (1970). Application of line geometry to theoretical kinematics and the kinematic analysis of mechanical systems. J. Mechanisms 5, 3, 417–460.
21. Yuan, M. S. C. and Freudenstein, F. (1971). Kinematic analysis of spatial mechanisms by means of screw coordinates: Part 1 — Screw coordinates. J. Engineering for Industry 93, 1, 61–66.
22. Zhao, J., Li, B., Yang, X. and Yu, H. (2009). Geometrical method to determine the reciprocal screws and applications to parallel manipulators. Robotica 27, 6, 929–940.