ackermann steering most vehicle steering systems use some form of the ackermann steering model. for...
TRANSCRIPT
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?