Adjust double wishbone or MacPherson strut geometry in real time and visualize camber angle, track width change, and roll center height vs wheel travel.
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.
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.
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.
The calculation results from this tool are not self-contained; they become input information for the entire field of Vehicle Dynamics. For example, the roll center height determined here is used directly in calculating the vehicle's roll stiffness (anti-roll bar design) and load transfer during roll. A high roll center increases the "jacking force" generated at the tires during cornering, which affects steering feel and limit handling characteristics.
It is also deeply connected to Durability & Strength Analysis (Durability CAE). The positions of the arm mounting points (hardpoints) decided in the simulator are the primary determinants of the forces acting on subsequent links and knuckles. For instance, a steep lower arm angle can generate large axial forces in the arm due to longitudinal forces during braking, increasing the risk of buckling. If you consider only strength while ignoring kinematics, you will misjudge the actual load conditions.
At a more advanced level, it connects with the field of Optimization Design (Design Exploration). The hardpoint positions that simultaneously satisfy multiple characteristics—like camber change, track change, and roll center locus—cannot be found manually. Therefore, methods are used where the calculation engine of this simulator serves as an "evaluation function," allowing a computer to automatically try thousands of variations to search for the optimal solution. This is the true essence of CAE-driven design.
The next step is to deepen your understanding from "Kinematics" to "Compliance Kinematics". This tool deals with pure geometry (kinematics), but in reality, "compliance kinematics," which considers bush elasticity, is crucial. For example, when lateral force is applied, bush deflection alone can change the camber angle by 0.5 degrees or more. To study this field, learning analysis methods using Multi-Body Dynamics (MBD) software becomes the next challenge.
Regarding the mathematical background, the geometry of vectors and coordinate transformations is fundamental. The equations shown earlier essentially derive tire orientation angles using the cross and dot products of vectors formed by points in space ($P_u$, $P_l$, $P_t$). To handle more general linkage mechanisms, robotics methods like Screw Theory and Denavit–Hartenberg forward kinematics become powerful tools. These theories are useful when analyzing complex suspensions (like 5-link types).
For practical learning, try challenging yourself with the "inverse problem" of setting a "target characteristic curve" in this simulator and working backwards to determine the hardpoints. For example, from a requirement like "achieve -2 degrees of camber at 50mm of bounce," how should you decide the arm lengths and mounting point heights? Through this trial and error, you can gain an intuitive understanding of the sensitivity of each parameter (which parameter has the most effect). This is the first step in growing from an "engineer who calculates" to an "engineer who designs."