Ackermann Steering

• Most vehicle steering systems use some form of the Ackermann Steering model.

• For turning stability tires will turn on different radii.

Ackermann Steering

Ackermann Steering

Research

• First step was to research steering geometries and types of mechanism suitable for our requirements.– Cheap– Rugged– Easily maintained – Readily available parts

Mechanism Selection

• Mechanism should provide moderate responsiveness and ease of operation

– Best choice – Recirculating Ball Steering Mechanism

Mechanism Elimination

• Hydraulic

– Failed Ease of Maintenance and availability of parts.

• Rack and Pinion

– Failed ease of operation at low speeds

Rough Geometry• Due to the suspension design I was required

to follow the following setup.

Geometry

Geometry

Geometry

Equations

Resulting in an equation for the tie rod length based on c the distance to the center link from axis of rotation of the tires.

Left Side Equations

Where

Right Side Equations

Where

EquationsVariable Description

a Distance from knuckle to center link

b Travel of center link

c Distance from center link to axis of rotation

x Length of steering knuckle

y Tie rod length

Angles between steering knuckle and tire

Angle between knuckle and axis of rotation on

the left side

Angle between knuckle and axis of rotation on

the right side

Left turn angle

Right turn angle

Program• #include <stdio.h>• #include <math.h>• #include <conio.h>• int main(){• float y, c, b;• double x= 6.403;• double P, Q, R, Theta1, Gamma1;• double I, J, K, Theta2, Gamma2;• printf("Input value for y: ");• scanf("%f", &y);• printf("Input value for c: ");• scanf("%f", &c);• printf("Input value for b: ");• scanf("%f", &b);• printf("The values entered are: %f, %f, %f\n", y, c, b);• float a = 20.1797;• float g = 20.1797;• float pi = 3.141592654;• printf("a equals: %f\n", a);• printf("g equals: %f\n", a);• R = pow(y,2) - pow(x,2) - pow(b,2) - pow(a,2) - pow(c,2) - 2*a*b;• Q = 2*x*c;• P = 2*x*(a+b);• K = pow(y,2) - pow(x,2) - pow(b,2) - pow(g,2) - pow(c,2) + 2*g*b;• J = 2*x*c;• I = 2*x*(g-b);

Program• I = 2*x*(g-b);• printf("P equals: %f\n", P);• printf("Q equals: %f\n", Q);• printf("R equals: %f\n", R);• printf("I equals: %f\n", I);• printf("J equals: %f\n", J);• printf("K equals: %f\n", K);• double den1, den2;• double den3, den4;• den1 = sqrt( pow(P,2) + pow(Q,2) ); //denominator• den2 = den1; //both denominators are the same• den3 = sqrt( pow(I,2) + pow(J,2) ); //denominator• den4 = den3; //both denominators are the same• Theta1 = ((1 / cos((R/den1)*(-1)) - 1 / cos(P/den2))*(180/pi));• Theta2 = ((1 / cos((K/den3)*(-1)) - 1 / cos(I/den4))*(180/pi));• printf("Theta1 equals: %f\n", Theta1);• printf("Theta2 equals: %f\n", Theta2);• Gamma1 = (90 - 38.66 - Theta1);• Gamma2 = ( -90 + 38.66 + Theta2);• printf("Gamma1 equals: %f\n", Gamma1);• printf("Gamma2 equals: %f\n", Gamma2); • getch ();• return 0;• }

Sample Input Valuesc y b

1 16.66685 0.5 1 1.5 2 2.5

2 16.45552 0.5 1 1.5 2 2.5

3 16.30289 0.5 1 1.5 2

4 16.21063 0.5 1 1.5 2

5 16.17976 0.5 1 1.5

6 16.21064 0.5 1 1.5

7 16.30292 0.5 1

8 16.45556 0.5 1

Final Geometry

• Through many program runs, hand calculations and AutoCAD drawing I was able to establish that by placing the center link 4 inches from the axis of rotation and with a tie rod length of 16.21063 I could achieve turn angles of

• With the smallest error of 0.2068 inches

Final Geometry Turn Radii

◦ 7.15 ft. (Inside)◦ 11.87 ft. (Outside

Parts

Component Quantity Manufacturer Specifications Recirculating

Steering Mechanism

1 Siganaw 24:1 Gear ratio

Center Linkage 1 Duralast Complete with 2 Nuts, 2 Cotter Pins, 2 Grease

Fittings, 2 Sponge Seals

Tie Rod Ends 4 Duralast Complete with Nut, Cotter Pin,

Zerk Steering Knuckle 2 51.34 Degree

angle with hub assembly

Idler Arm Assembly

1 Wenzhou Tentec Comes with mounting bracket

Pitman Arm 1 Duralast Comes with grease fitting, Nut, Cotter Pin, Sponge Seal

Tie Rod Adjusting Sleeve

2 Duralast Complete with 2 locknuts and 2

bolts Grease Boot 4 Summit Racing 2 per pack

Steering Shaft 1 Summit Racing 36” Long Double D

Universal Joint 1 Summit Racing Max angle 40 degrees

Support Bearing 1 Summit Racing ¾ in bore

Constructed System

Deliverables

Mechanism SelectionRough Geometry SelectionGeometric Equation ResearchC++ ProgramCalculations of Ackerman AnglesFinal GeometryConstruction

Conclusion

Questions?