Suspension Kinematics Simulator Back
Automotive Engineering

Suspension Kinematics Simulator

Adjust double wishbone or MacPherson strut geometry in real time and visualize camber angle, track width change, and roll center height vs wheel travel.

Suspension Setup

Upper arm length (mm)
mm
Lower arm length (mm)
mm
Upper mount height (mm)
mm
Lower mount height (mm)
mm
Wheel travel (mm)
mm
Static camber (°)
°
Results
Current camber
-1.5°
Track change
0 mm
Roll center height
95 mm
Scrub radius
18 mm
Susp
Camber
Track

What is Suspension Kinematics?

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What exactly is suspension kinematics, and why is it so important for a car's handling?
🎓
Basically, it's the study of how the wheel moves relative to the car's body—not from forces, but purely from geometry as the suspension compresses or extends. In practice, this controls critical things like how much the wheel tilts (camber) during a turn. Try moving the "Wheel Travel" slider in the simulator above; you'll see the wheel's angle change instantly, which is the core of kinematics.
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Wait, really? So the geometry itself decides the camber? What's the "roll center" I see in the simulator then?
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Exactly! The lengths and pivot points of the control arms define the motion. The roll center is a key imaginary point. Think of it as the pivot point around which the car body rolls during cornering. A common case is a sports car, where engineers want a high and stable roll center for flat cornering. In the simulator, adjust the "Upper Arm Length" and see how the roll center height line moves dramatically.
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The FAQ mentions "scrub radius." That sounds technical. How does it affect what I feel when driving?
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Great question! Scrub radius is the lateral distance between where the steering axis hits the ground and the center of the tire's contact patch. For instance, in car crash tests or during hard braking, a large scrub radius can make the steering wheel pull sharply to one side. In the simulator, play with the "Kingpin Inclination" slider. You'll see the steering axis tilt and directly affect the scrub radius calculation, showing why most street cars aim for near-zero scrub.

Physical Model & Key Equations

The core of suspension kinematics is analyzing the rigid body motion of the wheel assembly, connected by two control arms (for a double wishbone) or a strut and a control arm. The position of the wheel center is determined by the intersection of spheres defined by the arm lengths.

$$ \vec{P}_{wheel}= \vec{P}_{upper}+ L_{u}\hat{u}= \vec{P}_{lower}+ L_{l}\hat{l}$$

Where $\vec{P}_{wheel}$ is the wheel center point, $\vec{P}_{upper}$ and $\vec{P}_{lower}$ are the inner pivot points on the chassis, $L_u$ and $L_l$ are the upper and lower arm lengths, and $\hat{u}$ and $\hat{l}$ are the unit vectors along the arms. Solving this constraint gives the wheel's position for any given suspension travel.

Camber angle $\gamma$ is a direct output of this solved geometry. It's the inclination of the wheel plane from the vertical. The instantaneous roll center is found geometrically by intersecting lines through the instant centers of the control arms.

$$ \gamma = \arctan\left(\frac{\Delta y}{\Delta z}\right) $$

Here, $\Delta y$ and $\Delta z$ are the lateral and vertical displacements of the top and bottom of the wheel. A negative $\gamma$ during compression (top tilting in) is often desirable for maintaining tire contact during cornering body roll.

Real-World Applications

Performance Vehicle Tuning: Race engineers obsess over kinematics. They adjust pickup points on the chassis to fine-tune camber gain, ensuring the tire remains flat on the track during high-G corners for maximum grip. The simulator's "Arm Length" sliders directly mimic this tuning process.

Off-Road & SUV Development: For vehicles that need massive wheel travel, kinematics ensures the tire doesn't tuck in too far or hit the fender. A key goal is managing the drastic change in track width, which you can visualize with the "Track Width Change" plot in the tool.

Electric Vehicle Packaging: EVs often have a flat battery pack in the floor. Suspension geometry must be designed around this hard point to achieve desired kinematics without compromising ground clearance or battery safety, making virtual simulators like this essential.

Brake System Integration: As mentioned in the FAQ, scrub radius is critical. Engineers use kinematic models to minimize brake steer, where uneven braking forces cause unwanted steering pull. This is vital for safety and driver confidence in all modern cars.

Common Misconceptions and Points to Note

First, understand that "good values" change depending on the situation. For example, aiming for camber change to be close to "zero" is not always the correct answer. Racing cars are designed to achieve strong negative camber during bounce to pursue ultimate cornering performance. Conversely, for general passenger cars, the amount of change is kept small to prevent uneven tire wear. Before trying to draw an "ideal curve" in the simulator, first consider "what is the intended use of this vehicle?"

Next, there is the pitfall that parameters are not independent. Changing the length of the upper arm will change the camber curve, but it will also move the roll center height simultaneously. For instance, if you lengthen the upper arm by 10mm to improve camber characteristics, the roll center might rise by 5mm, potentially causing other effects on handling stability. In practice, it's a battle against these trade-offs. When you adjust one parameter, make it a habit to always check all other outputs.

Finally, don't forget that the simulation calculates for "ideal rigid bodies". Actual suspensions have bush compliance, arm stiffness, and even deformation of the tire itself under load. Even if you achieve perfect characteristics in the simulator, if real-world testing shows "more roll than expected," you need to suspect the influence of bush compliance (flexibility). Remember, this tool is the first step in determining the "geometric skeleton," followed by CAE analysis that considers component elasticity.

How to Use

  1. Enter upper control arm length in mm (typical range 300–450 for double wishbone) using v-upper slider or s-upperNum numeric input
  2. Set lower control arm length in mm (typical range 350–500) via v-lower and s-lowerNum controls
  3. Define upper mounting point offset from wheel centerline in mm using v-umount and s-umount to establish kingpin inclination
  4. Adjust wheel travel range in mm to observe real-time camber curve, track width change, and roll center migration across suspension stroke
  5. Compare geometry outputs: negative camber gain, anti-dive percentage, and scrub radius to OEM benchmarks

Worked Example

Double wishbone sedan suspension: upper arm 320 mm, lower arm 380 mm, upper mount offset 85 mm from wheel center. At 0 mm ride height, camber reads -0.2°; at +50 mm jounce (compression), camber drops to -1.8° with roll center height rising 12 mm. Track width increases 3.2 mm over 100 mm travel. With 12 kN vertical load applied, anti-dive geometry yields 15% anti-dive, reducing front-end dive under braking from nominal 45 mm to 38 mm over 1 m stopping distance.

Practical Notes

  1. Shorter lower arms increase camber sensitivity per mm of travel—race applications use 30–40 mm/100 mm to maintain tire contact patch; road cars target 8–15 mm/100 mm for tire wear balance
  2. Negative upper mount offset (inboard geometry) reduces kingpin inclination and scrub radius; verify against steering column packaging and tie-rod length constraints at full lock
  3. Roll center height below ground plane (negative value) at ride height indicates oversteer bias; adjust arm lengths symmetrically to shift roll center +5 to +15 mm for neutral handling
  4. Simulate bump steer by measuring toe change across 50 mm jounce; acceptable range is ±0.1° per 25 mm travel for passenger vehicles