calculations for a rack and pinion steering system used in BAJA

If you are using Ackermann steering geometry

1. Turning circle, link lengths & inclinations

Source: STEERING MECHANISMS | Kinematics of Machines Tutorials – Engineering Tutorials

Here’s an illustrative calculation…

The Ackermann Principle as Applied to Steering (Automobile)

2. Providing for required wheel turning angles in the steering linkage & wheel envelopes.

Source: Steering Systems (Automobile)
3. Steering ratio calculations

Source: ThyssenKrupp InCar®plus
4. Sizing of links and joints as per steering & road loads

Source: Steering Rack And Pinion Calculation Step-by-Step Plans

If it is not necessarily Ackerman geometry and you are undecided, have a look at this comparison……

How to Calculate forces coming on Knuckle

Steering knuckle is the most stress sustaining and critical component of All Terrain Vehicle (ATV). Steering knuckle is the pivot point of the steering and suspension system, which allows the front wheels to turn and also allow the movement of suspension arms motion. The light weight and high strength component is always in demanding for racecar application.
Lightweight and optimized design of steering knuckle is proposed to use for a BAJA SAE INDIA off road racecar. Due to the failure in knuckle in terrain vehicle after some instances, it has to be modified for better performance. The 3D CAD model created by using CATIA V5 and static as well as model analysis carried out in ANSYS 12 to understand its behavior under operating conditions. All test for frame was carried out on aluminum alloys 6061-T6 & for spindle EN8. The paper discusses the FE analysis of existing and modified Steering Knuckle.

Calculation of Load:

Axial Loads
The two major loads acting on the knuckle are Tensile and
Compressive loads. The stresses due to these loads can be
determined using the following formulas
Tensile Load (Pt) = Tensile Stress X Area
Compressive Load (Pc) = Compressive Stress X Area
Inertia Load
This load is due to the inertia of the moving parts. To calculate
the inertia force, first two harmonies are taken into
consideration. It is given by,


Ackerman percentage, IBJ and OBJ center distance – Steering Explained

Question asked – 
We are intended to use nano steering. We were having problems regarding Ackerman percentage, IBJ and OBJ center distance. Kindly explain
obj- outer ball joint

ibj – inner ball joint.

steering has two ball joints……and in most of the Baja vehicle are used centralized steering so its ibj and obj for both left and right is same but for nano car it will be different for left and right. mainly ibj change obj remains constant because of selective assembly principle

Attached here are the two PDF whitepaper which will give you in-depth insight.



Steering & Wheel Alignment

What is ackerman angle?

It is used in the concept of ackerman steering. While going around a corner all the tires turn along the circle with a common center point(as shown in figure). The intention of Ackerman geometry is to avoid the need for tyres to slip sideways when following the path around a curve. The angles b and a can be calculated by



Calculations for the Anti Ackermann Steering Mechanism

let me qualitative describe anti-Ackermann steering. In order to do this I will start with a description of Ackerman steering which forms the basis for Anti-Ackermann steering.

In 1818, Rudolf Ackerman  patented a design of Georg Lankensperger that provided a steering system for carriages that eliminated the angle scrub and subsequent wear of the wheels on the front axle. While not intellectually right to Mr. Lankensperger, I rather glad we don’t call this system Lankensperger steering!  The assumption was made that a carriage would rotate in a turn by a center somewhere along the line of the rear axle, that the outer front wheel had to turn faster and at a greater angle than inner front wheel and that the plane of  front wheels would perpendicular to the radial axis to center of the turn. The assumptions made in Ackermann steering are:

  • No lateral forces
  • No wheel compliance
  • No body roll
  • Only front wheels contribute to steering
  • No suspension effects
  • No longitudinal weight transfers
  • Constant speed


Ackerman steering is normally computed using  a Jeantaud diagram (Charles Jeantaud in 1878 created a geometrical method to arrive at Ackerman steering) where the equal length steerings arms are placed on a line connecting the wheel center and the center of the rear axle:

What this is a special case of trapezoidal steer which is a four bar linkage:

Solving this for the the condition of the outer front wheel we get

Then we can ask, what are the requirements for Ackermann angle:

As you can see, we can only approximate true Ackermann steer to within a small steer. Normally, in Vehicle Dynamics, where computational accuracy can be sacrificed for simplicity, the Ackermann steer angle is computed by

Anti-Ackermann was devised, mainly for race cars to gain a steering advantage in tight turn race courses where increased outer wheel steering angles are needed. Anti-Ackermann steer is usually computed using the a “horizontally flipped Jeantaud diagram:

(borrowed from…

The computation are essentially the same as above.

Steering Wheel for BAJA SAE

If you are looking for Steering wheel that fits into your BAJA Buggy. It is best advisable to make your own.
Try making it from Balsa Wood or Carbon Fibre, these are significantly lighter too.

There are many different ways of making it, but if this is going to be your first experience with composites, we would recommend you start with something easier. Flat panels for skidplates or number panels are the easiest to learn on, and most forgiving. Complicated geometry with complex loadings like a steering wheel should be reserved for when you are comfortable working with the materials and have a good idea about what is good and bad for it structurally.

Here is a short video of Formula SAE(FSAE) – Carbon fiber steering wheel fabrication :

How To Make Your Own Carbon Fiber (Fibre) Parts. –

To go with the pre-made aluminum Steering wheel –

Design Processes & Analytical Explanations of Baja.Student.India


Car 99 cad model.
Car 99 cad model.

The function of the steering system is to steer the front wheels in response to driver command inputs in order to provide overall directional control of the vehicle.

Rack with centrally placed pinion manufactured with sand parts is chosen with following

Rack length = 279.4mm,
Weight = 1.02Kg,
Rack travel = 257.15mm (centre to lock), Pinion travel = 270 degrees (centre to lock).

Ackerman steering geometry is used to change the dynamic toe setting, by increasing front wheel toe out, as inside wheel is steered to a greater angle than the outside wheel.

1) Advantages of Ackerman Geometry;

The advantages of the Ackerman Geometry is that during a turn outer front wheel maximizes its tyre grip, at the expense of inside tyre grip, in a negative camber carrying front tyres, Ackerman geometry helps to compensate for negative camber on the inside tyre.

Ackerman helps to reduce tyre wear by providing common centre of rotation for all the four wheels. The inner and outer wheels have different angle displacement which helps to gain common turning centre.

As lighter the tyre load, the higher the slip angle required for peak cornering power, Ackerman geometry is beneficial.

2) Analysis of Tie Rod; Several forces will act on tie rod

1. Axial Compressive force (which is reaction of steering force) of magnitude 544.88 N 2. Bump force (which will act perpendicular to
axial force) of magnitude 1.5G (4267.35 N)

Alloy steel is selected as material of tie rod having yield strength 250MPa. Tie rod analysis by using ANSYS software shows that the maximum deformation is 0.00005627mm and equivalent stress (Von-misses stress) is 25.4MPa which is less than tensile and compressive yield strength i.e. 250MPa.




Turning Radius(m) 3.13
Max. Turning Angle(degrees) 40
Ackerman Angle(degrees) 31
Steering ratio 8.11

For any queries please contact us on-,,


Since our main focus is towards their use in an ATV, this article deals with the pros and cons of both the joints in an ATV. For those who have no idea about these two joints, the pictures below shall feed their brains.

Ball Joint
Helm Joint







Ball joints are strong up and down but have limited angular movement. The ball and socket joint in human body that connects our leg bone to your hipbone, so goes the ball and socket joint that holds the front suspension of your vehicle together.  Your leg can move up and down, and side to side, the automotive ball joint enables the wheel and suspension to move together in the same manner. If you try to increase the angular movement, it may result it in weakening the joints to pull-out force since the cup doesn’t cover the ball’s neck area much. These require very less maintenance. They last longer and are cheaper than their counterpart. Most often well sealed Tie rod ends are used as ball joints. They have high serviceability but the Z-axis force is still less. These may also have springs under the cup to take up wear. This makes them good to use for tie rod ends but poor for ball joints.

Heim joints are known to be a little weaker, but with the correct offset spacers, they can reach much farther angles than ball joint. Camber/caster adjustments are relatively easier. Using it may be a boon/ curse as it depends on the accuracy of the suspension design. But perpendicular to the shafts (Z axis) they are comparatively weak. With boots, Heim are reliable. But without it, grits get into them and wears out easily.

To summarize, the heim joints shall be used where end to end use, serviceability is preferred and the

Ball joints shall be used where strength, low maintenance and life is given the first preference.

Ref- Replacing Ball JointBall joint maintenanceBall JointHistory of Heim JointHeim Joint