A pure trailing arm is pivoted to the vehicle structure at its forward end and supports a wheel or axle at its rear end. In a rigid two-dimensional idealization with a fixed lateral pivot axis, the wheel centre follows a circle about that pivot.
Trailing Arm Suspension Interactive Calculator
Enter a rigid pivot-to-wheel-centre length and upward vertical displacement from a horizontal arm datum. Results describe one ideal circular arc only, not a complete suspension.
Equation Used
- The arm is rigid and has fixed pivot-to-wheel-centre length L.
- The pivot is fixed and its axis is perpendicular to the side-view plane.
- The reference arm position is horizontal and entered dz is upward displacement from that datum.
- Entered displacement remains below arm length across the provided input range.
- Compliance, spring and damper geometry, tire radius, stops, clearances, camber, toe, roll, loads and dynamics are omitted.
Fixed Pivot and Circular Wheel-Centre Path
Trailing-arm suspension patents describe an arm extending generally in the vehicle's longitudinal direction, pivoted to the vehicle structure at its forward or proximal end and connected to a wheel carrier or axle at its rear or distal end. For a pure trailing arm, the pivot axis is substantially lateral and the arm pivots in the vehicle's vertical direction.
If that arm is treated as rigid and the pivot is fixed, its wheel-centre point remains one arm length from the pivot and therefore follows a circle in side view. Semi-trailing, compliant, linked or sliding-pivot designs require different geometry.
What This Calculator Does
The tool resolves the ideal wheel-centre coordinates after an entered upward displacement from a horizontal arm position. It reports horizontal recession, arm angle, distance travelled along the circular arc and the difference between arm length and entered vertical displacement.
It does not calculate real suspension travel, packaging clearance, camber, toe, spring motion ratio, load, handling or durability.
Rigid Side-View Circle Geometry
dx = L-x
theta = asin(dz/L)
s = L theta
rz = L-dz
Angle theta is in radians in the arc-length relation and converted to degrees for display. The relation assumes 0 less than or equal to dz less than L.
Worked Ideal Example
For L=450 mm and dz=150 mm from the horizontal datum, the horizontal recession is about 25.7 mm, the arm rotation is about 19.5 degrees, and the wheel-centre arc distance is about 152.9 mm. The vertical geometric-domain reserve is 300 mm.
That reserve is not a statement about available bump travel or physical clearance.
Model Boundary
- Mechanical arrangement: a longitudinal arm has a forward vehicle pivot and a rear wheel or axle connection; a pure arm pivots substantially in the vertical direction about a lateral axis.
- Calculated: one rigid circular path in side view from a horizontal datum.
- Not calculated: actual static arm angle, three-dimensional pivot-axis inclination, semi-trailing geometry, multiple links, sliding pivots, bush compliance, camber, toe, track, wheelbase, tire deflection, spring or damper motion ratio, anti-squat, roll steer, braking, force, stress, fatigue, clearance, stops, alignment, stability, ride, handling, durability or safe design.
Frequently Asked Questions
Does every trailing-arm suspension follow this path?
No. The model is only a rigid pure trailing arm with a fixed pivot and horizontal reference position.
Is the recession measured from the road or chassis?
It is the horizontal coordinate change relative to the fixed pivot in the ideal side-view diagram.
Why is arc distance slightly larger than vertical displacement?
The wheel centre moves along a circle, while vertical displacement is only one component of that motion.
Is the vertical reserve usable bump travel?
No. It only shows L-dz relative to the mathematical limit dz=L.
Does the model predict camber or toe?
No. Those require three-dimensional geometry and compliance information.
Can the outputs be used to modify a vehicle suspension?
Not by themselves. Vehicle suspension work requires complete geometry, structural and dynamic analysis, applicable requirements and qualified professional review.
References
- U.S. Patent 7,520,516, Suspension trailing arm: longitudinal arm, wheel-side axle carrier and substantially lateral pivot axis permitting vertical arm motion.
- U.S. Patent Application 2008/0252031, Leading and trailing arm suspensions with Z-shaped arms: proximal frame pivot, distal axle connection and the axle-behind-hanger trailing-arm definition.
- U.S. Department of Transportation report, Figure D-12: comparison sketches for trailing arm, semi-trailing arm, swing axle and other suspension layouts.
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