Model and calculation method
Which points are needed?
Both axles determine scale and image orientation. The bottom bracket locates the chainring. Main pivot, Horst pivot, seatstay/rocker pivot and rocker/frame pivot form the four-bar linkage. The rear axle is fixed to the seatstay link. Both shock eyes determine shock compression. The Horst pivot is ahead of and below the rear axle.
Leverage Ratio
LR = d(vertical rear-wheel travel) / d(shock compression)
The instantaneous ratio follows from linkage velocities and shock shortening. LR = 3 means locally 3 mm of vertical wheel travel per 1 mm of shock compression. A decreasing ratio is commonly described as progressive kinematics. The air or coil spring curve itself is not included.
Anti-Squat
The instantaneous centre is the intersection of the extended main-pivot–Horst-pivot and rocker-frame–seatstay-pivot lines. The upper chain tangent intersects the rear-axle–instantaneous-centre line at the instantaneous force centre (IFC). The line from rear tire contact through the IFC is evaluated at the front axle's vertical line. Its height above rear tire contact, divided by the current relative centre-of-mass height, gives anti-squat as a percentage. The selected gear therefore changes the curve.
Anti-Rise
Here the force line runs from rear tire contact directly through the instantaneous centre. The percentage uses the same height ratio as anti-squat. This assumes rear-wheel-only braking and a brake attached to the axle-carrying link. In the idealised model, 100% means full compensation of extension caused by load transfer; it does not rate overall braking performance.
Construction in the diagram
The slider below the drawing selects any calculated travel position. The optional construction shows how both values arise there: the extended link axes and their intersection (instantaneous centre), sprocket and chainring circles with their upper tangent, the instantaneous force centre (IFC) on that tangent, and both force lines from the rear tire contact point. On the vertical above the front axle, the reference height h₀ − travel is drawn as the 100% mark; the dots on it are where the force lines cross and match the displayed percentages exactly. Instantaneous centre, force centre and crossings often lie outside the photo and are then clipped — an anti-squat above 100% crosses above the mark. Once all nine points are placed, the marking input can be minimized so that only the drawing, slider and construction remain visible.
Assumptions and limits
As in the thesis, the main frame stays fixed. The overall centre-of-mass reference height decreases relative to rear tire contact by vertical wheel travel: h(s) = h₀ − s. This does not simulate actual frame pitch or fork motion. Links are rigid and backlash-free; wheels have equal sizes, the upper chain run has no idler, and the shock is mounted on the rocker. The pitch-circle approximation follows the MATLAB model: r = 2.024 × tooth count in mm.
Perspective distortion, hidden pivots and an already compressed bicycle affect results. Prefer an orthogonal side view or a dimensionally accurate drawing. Points can be edited to 0.1 image pixel, but accuracy depends on the photo. Toggles, wheel-travel reversal and shock limits stop the analysis; the displayed endpoint is the last valid sample. Collisions, strength, dynamic riding loads and automatic optimisation are outside this initial analysis version.
Sources and implementation
Florian Schmidt (2020): Entwicklung eines Optimierungsalgorithmus für die kinematische Auslegung eines Mountainbike-Fully-Rahmens, TU Dresden, 17.07.2020, chapters 2.4, 4.2–4.3. MATLAB: kin_analyse_viergelenker.m (provided by the author).
Additional explanation of leverage curves: Vorsprung Suspension – Understanding Leverage Curves (accessed 08.09.2026).
The web version preserves the model assumptions and replaces slope divisions and forward differences with vector geometry and instantaneous velocities. It is not an unchanged MATLAB port or a standards compliance assessment.