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12th IFToMM World Congress, Besanon , June18-21, 2007 Id-814

Kinematic Analysis of Front Suspension of an Automobile and Prediction of

Steering Behaviour

J.P.Modak * P.N.Belkhode

Professor in Mechanical Engg. & Dean (R&D) Lecturer in Mechanical Engg. , PCEA Nagpur, Maharashtra, India PIET Nagpur Maharashtra, India

Abstract The suspension comprises of a linkagewhich is a 3 Dimensional mechanism SCCS (Spherical,Cylindrical, Cylindrical, Spherical paired). On the basis of sixincluded angles of this four bar chain, position of kingpin axis isdetermined. Once the position of kingpin axis is decided

corresponding kingpin angle, caster angle, camber angle can bedetermined. Position of kingpin axis is determined using Denavit Hertenberg principle. This paper details the steering geometry of anautomobile. Appropriate ness of special bushes is based on thebehaviour of the steering geometry which can be predicated bykingpin angle, caster angle, camber angle and steer angle. It isan article proposing how to perform experimentation for front

suspension of an automobile.

Keywords: Camber angle, caster angle, kingpin angle, steering geometry, front suspension

I. Introduction

It is essential to decide appropriateness of special bushes, which are used at various joints of suspension.This appropriateness of special bushes is based on thesteering performance. Steering performance depends onthe position of kingpin axis. Depending on the position of kingpin axis caster angle, camber angle, kingpin angle andsteer angle of four wheel vehicle is decided. Experimentalsetup is also proposed evolved to locate these angles. Onthe basis of six include angles of this four bar chain SCCS

position of kingpin axis is determined.Joint variation can be acertained using the

proposed experimental Testrig. Kinematic analysis of steering geometry can be decided based on behavior of

front suspension [1]. Proposed experimental setup canmeasure the corresponding angles of steering geometry.

II. Front suspension and steering geometry:A front Suspension basically comprises of a linkage

which is a 3D four bar chain SCCS (Spherical,Cylindrical, cylindrical, Spherical) as shown in Fig 1.Joint O 1 and O 2 are spherical joints and joints A and B arecylindrical joints [2].

*E-mail: [email protected] E-mail: [email protected]

The important element of a steering system consistsof linkage and geometry associated with the steer rotationaxis at the road wheel. This geometry affects the overall

performance of vehicle. Refering figures 1 &2.

Fig 1: The A arm Front Suspension

A. Kingpin axis : The steer angle is achieved byrotation of the wheel about a steer rotation axis.This axis is kingpin axis.

B. Kingpin inclination angle: The angle in frontelevation between the steering axis and thevertical.

C. Caster angle: The angle in side elevation betweenthe steering axis and the vertical.

D. Camber angle: The Inclination of the wheel planeto the vertical

C

O1

O2

A

B

C

S

S

Kingpin Axis

Center of TireContact

Kingpin Offset at the Ground

Kingpin InclinationAngle

Caster Angle

Fig 2: Steer Rotation Geometry at the Road Wheel
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IV. Deduction of steering behaviour:

A. Position of Joint A and Joint BConsidering joint A as origin, the two included angles at

joint O1 is 1, 1 and r1 as link O1A.Spherical joint O1 = Position at joint A with spherical O1 + Rotation at joint A respect to O1

Cylindrical joint A = Position at joint B with cylindrical A + Rotation at joint A with respect to B

Transformation matrix at joint A with respect O1, O2, & B

Ax = r1 C 1S1 d1Ay = r1 S 1S1 r3 C 3 Position of Joint AAz = r1 C1 + r3 S 3

r1 = L1 = 25.40 cmd1 = X = 6.35 cm Dimension of front suspension of r3 = L4 = 30.48 cm a Scorpio vehicle of M&M(India)

Suppose include angle at O1, 1= 3 0 & 1 =5 0 and at A 3 = 4 0

Then, Ax = 8.56 cm , Ay = 30.52 cm and Az = 27.43 cm

Similarly, the two included angles at joint O2 is 2, 2 andr2 as link O2B.

Spherical joint O2 = Position at joint B with spherical O2 + Rotation at joint B respect to O2

Cylindrical joint B = Position at joint A with cylindrical B + Rotation at joint B with respect to A

Transformation matrix at joint B with respect O1, O2, & A

Bx = r2 C 2S2 r4 C 4By = r2 S 2S2 + d2 Position of Joint BBz = r2 C2 + r4 S 4

r2 = L3 = 38.10 cmd2 = X = 6.35 cm Dimension of front suspension of r4 = L4 = 30.48 cm a Scorpio vehicle of M&M (India)

Suppose include angle at O2, 2= 4 0 & 2 =5 0 and at B 4 = 6 0

Then, Bx = -9.62 cm , By = - 30.71 cm and Bz = - 37.29 cm

B. Vehicle reference frame

Fig. 6 : Vehicle reference frame The ground fixed reference frame with the axis x 0, y0,z0 and vehicle fixed reference frame the x F axis pointsforward, the y F axis to the left and the z F axis upward. Thewheel rotates around an axis which is fixed to the wheelcarrier. The reference frame C is fixed to the wheelcarrier. In design postion its x C, yC and z C are parallel tothe corresponding axis of vehicle fixed reference frame F[4].

C: Kingpin axis Location:

Fig. 7 : Wheel rotation axis

O1TA =

0 r1 C 1S 1-101 r1 S 1S 1000 r1 C 10-10 100

B T A =

1 - r3 C 3000 - r3 S3010 d1100 100

O2, O1, B TA =

0 r1 C 1S 1 d1-101 r1 S 1S 1 r3 C 3000 r1 C 1 + r3 S 30-10 100

O2TB =

0 r2 C 2S 2001 r2 S 2S 2-100 r2 C 20-10 100

A TB =

1 r4 C 4000 r4 S4010 -d2100 100

O2, O1, A TB =

-1 r2 C 2S 2 r4 C 4000 r2 S 2S 2 + d2-100 r2 C 2 + r4 S 40-10 100

Kingpin Axis

Joint A

Joint B Yc

Zc

Xc

a b

cd

e f

h

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D : Determination of kingpin and caster angle :

Kingpin Angle:Angle adb = Angle between the Zc axis and the projection line of thewheel rotation axis into Zc and Yc plane.

Caster Angle:Angle adh = Angle between the Zc axis and the projection line of thewheel rotation axis into Zc and Xc plane.

Kingpin angle = 43.4 0 and Caster angle = 15.67 0

V. System design of an experimental setup :

The relative orientation of two links connected atcylindrical joint can be decided by potentiometer /encoders and associated Opto electronics instrumentation.Six potentiometers located at four joints (two sphericaland two cylindrical) of the SCCS mechanism. Sixincluded angles of these SCCS mechanism are located bythe six potentiometers. At spherical joint O1 it measuresthe two included angles 1& 1 and a t spherical joint O2 itmeasures the two included angles 2 & 2 [5].At cylindrical joint A and B it measure angles 3 and 4respectively and linear displacement at A & B by LVDT [6].

Once these angles and displacement of linkage of frontsuspension are decided along with a link length, positionof kingpin axis can be located. According to the variationin front suspension, correspondingly angles of frontsuspension are measured through the interfacing program.Program is ready with input parameter such as sixincluded angles, two linear displacement at A & B andlink lengths of four bar chain. Using above detailedanalytical model position of joint A and joint B can bedecided. Thus the position of kingpin axis gets decided.Then corresponding kingpin angle, caster angle, camber angle and steer angle calulated by the program. Dynamic model of front suspension of automobile withimaginary 3D mechanism have been formulated usingCAD software [7]. Accoding to front suspensionmovement position of kingpin axis is varying andcorresponding kingpin angle, caster angle, camber angleand steer angle are varying.

V. Conclusion

The paper reports as a possible approach of decidingexperimentally kinematic analysis of a front suspension3D mechanism of an automobile. The paper detailsanalytical modelling for deciding position of kingpin axisin space in terms of experimentally decided joint anglesand displacements at joints. An approach to decide theseangles and displacements experimentally is also included.

Once the position of kingpin axis is known the complete

steering geometry can be decided. This is very useful for deciding performance of various synthetic rubber bushesused at various joints of front suspension.

References [1] Alonzo Ketty, Essential Kinematics for Autonomous Vehicles , The Robotics Institute Carnegie Mellon University, 5000 Forbes Avenue Pittsburgh, PA 15213, May 2, 1994. [2] T. D. Gillespie, Fundamentals of vehicle Dynamics , Society of Automotive Engineers, Inc. Warrendale, PA 15096-0001. [3] K.S. Fu, R.C.Gonzalez, C.C.G.Lee, Robotics: Control, Sensing , Vision and Intelligence , Mc graw hill Internation Edition, Signapore. [4] Prof. Dr. Georg Rill, Vehicle Dynamics , Fachhochschule

Regensburg, University of Applied Sciences, Hochschule For Technik Wirtschaft Soziales. [5] Dipl.-Ing. Mathias Wilmes, Thomas Horrman, Automotive E ngineer II Kinematics and Compliance Test Rig , Aachen, April 2006. [6] L.Song, X. Qu, K.Xu, L.Lv, , Three Dimensional Measurement and Defect Detection Based on Single Image , Journal of Optoelectronics and Advanced Materials, Vol. 7, No.2, April 2005, PP 1029-1038.[7] Venture G., Khalil W., Gautier M., and Bodson P. , Dynamic

Modelling and Identification of a Car ,In 15 th IFAC World Congress, Barcelona, Spain, July 2002.

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