The steering gear mechanism is used for changing the direction of two or more of the wheel axles with reference to the chassis, so as move the automobile in any desired path. Usually the two back wheels have-a common axis, which is fixed in direction with reference to the chassis and the steering is done by means of the front wheels.

Figure 2.7 The steering gear mechanism

$cot\phi-cot\theta=\frac{c}{b}$

Where a = wheel track, b = wheel base, and c = Distance between the pivots A and B of the front axle. Types of Steering Gears There are mainly two types of steering gear mechanisms:

(a) Davis steering gear,

(b) Ackerman’s steering gear, Both these mechanisms are described separately as follows

1.Davis Steering Gear This steering gear mechanism is shown in Figure 2.8 (a). It consists of the main axle $AC$ having a parallel bar $MN$ at a distance h. The steering is accomplished by sliding bar MN within the guides (shown) either to left or to the right hand side. $KAB$ and $LCD$ are two bell-crank levers pivoted with the main axle at A and C respectively such that $\angle BAK$ and $\angle DCL$ remain always constant. Arms $AK$ and $CL$ have been provided with slots and these house die-blocks M and N. With the movement of bar $MN$ at the fixed height, it is the slotted arms $AK$ and $CL$ which side relative to the die-blocks M and N. In Figure , the vehicle has been shown as moving in a straight path and both the slotted arms are inclined at an angle $\alpha$ as shown.

Now suppose, for giving a turn to the right hand side, the base $MN$ is moved to the right side by distance x. The bell-crank levers will change to the positions shown by dotted lines in

Figure 2.8 (b). The angle turned by the inner wheel and the outer wheels are $\theta$ and $\phi$ respectively. The arms $BA$ and $CD$ when produced will meet say at I, which will be the instantaneous centre.

Figure 2.8 Davis Steering Gear

Suppose $2b$=Difference between $AC$ and $MN$,and $\alpha$ =angle AK and CK made with verticals in normal position .

$tan \alpha=\frac{b}{h}$......(1.1a)

$tan(\alpha+\phi)=\frac{(b+x)}{h}$ [considering point A]......(1.2b)

$tan(\alpha-\theta)=\frac{(b-x)}{h}$ [considering point C].....(1.2c)

Now, $tan(\alpha+\phi)=\frac{tan\alpha+tan\phi}{1-tan\alpha tan\phi}$

OR,$\frac{b+x}{h}=\frac{\frac{b}{h}+tan\phi}{1-\frac{b}{h}tan\phi}$

$b+htan\phi=(b+x)\frac{(h-btan\phi)}{h}$

$hb+h^2tan\phi=(b+x)(h-btan\phi)$

$hb+h^2tan\phi=bh+hx-b^2tan\phi+xbtan\phi$

$h^2tan\phi+b^2tan\phi+xbtan\phi=bh+hx-bh=hx$

$tan\phi=(h^2+b^2+xb)=hx$

$tan\phi=\frac{hx}{h^2+b^2+xb}$.........1.2(d)

Similarly, $tan(\alpha-\theta)=\frac{tan\alpha-tan\theta}{1+tan\alpha tan\theta}=\frac{b-x}{h}$

Studying for $tan\alpha$ and simplifying: $tan\theta=\frac{hx}{h^2+b^2-xb}$...............1.2(e)

After obtaining the expressions for $tan\phi$ and $tan\theta$, let us not take up the fundamental equation of steering: $cot\phi-cot\theta=\frac{h^2+b^2+xb}{hx}-\frac{h^2+b^2-xb}{hx}$

$cot\phi-cot\theta=\frac{2b}{h}=2tan\alpha$......1.2(f)

But for correct steering,

$cot\phi-cot\theta=\frac{a}{l}$

$2tan\alpha=\frac{a}{l}$

$tan\alpha=\frac{a}{2l}$...........1.2(g)

The ratio $a/ l$ varies from 0.4 to 0.5 and correspondingly $\alpha$ to 14.1 . The demerits of the Davis gear are that due to number of sliding pairs, friction is high and this causes wear and tear at contact surfaces rapidly, resulting in in-accuracy of its working.

Ackerman Steering Gear The Ackerman steering gear mechanism is much simpler than Davis gear. The difference between the Ackerman and Davis steering gears are:

1. The whole mechanism of the Ackerman steering gear is on the back of the front wheels; whereas in Davis steering gear, it is in front of the wheels.

2. The Ackerman steering gear consists of turning pairs, whereas Davis steering gear consists of sliding members.

The mechanism is shown in Figure 2.9 (a). This is simpler than that of the Davis steering gear system. It is based upon four-bar chain. The two opposite links $AC$ and $MN$ are unequal; $AC$ being longer than $MN$. The other two opposite links $AM$ and $CN$ are equal in length. When the vehicle is moving on a straight path link AC and MN are parallel to each other. The shorter links

$AM$ and $CN$ are inclined at angle $\alpha$ to the longitudinal axis of the vehicle as shown. $AB$ and $CD$ are stub axles but integral part of $AM$ and $CN$ such that $BAM$ and $DCN$ are bell-crank levers pivoted at A and C. Link $AM$ and $CN$ are known as track arms and the link $MN$ as track rod. The track rod is moved towards left or right hand sides for steering. For steering a vehicle on right hand side, link $NM$ is moved towards left hand side with the result that the link $CN$ turns clockwise. Thus, the angle $\alpha$ is increased and that on the other side, it is decreased. From the arrangement of the links it is clear that the link $CN$ or the inner wheel will turn by an angle $\theta$ which is more than the angle of turn of the outer wheel or the link $AM$.

Figure 2.9 Ackerman Steering Gear

To satisfy the basic equation of steering :$cot\phi- cot\theta= \frac{a}{l}$ the links $AM$ and $MN$ are suitably proportioned and the angle $\alpha$ is suitable selected. In a given automobile, with known dimensions of the four-bar links, angle $\alpha$ is known. For different angle of turn $\theta$, the corresponding value of $\phi$ are noted. This is done by actually drawing the mechanism to a scale. Thus, for different values of $\theta$, the corresponding value of $\phi$ and $cot\phi- cot\theta$ are tabulated. As given above, for correct steering, $cot\phi- cot\theta= \frac{a}{l}$
Generally, it is 0.455. In fact, there are three values of $\theta$ which give correct steering; one when $\theta= 0$, second and third for corresponding turning to the right and the left hand.