- How to measure
- What the results mean
- Link forces and strength
- Coilovers
- Gearing
- Formulas
- Where these calculators differ from the spreadsheets
How to measure
The link calculators use the same coordinate system as the Barcroft spreadsheets. Every point is in inches, measured with the vehicle at ride height, loaded the way it normally drives, on level ground.
- x: fore and aft
- Zero at the axle centerline (straight above the tire contact patch). Positive toward the front of the vehicle, so frame mounts ahead of a rear axle have positive x.
- y: side to side
- Zero at the vehicle centerline. Positive toward the driver side. For a pair of links, enter one side; the calculator mirrors the other.
- z: height
- Zero at the ground. Measure straight up to the center of each rod end, bushing or heim joint.
Tips
- Set the vehicle at ride height with its normal load, fuel and spare. Ride height changes every result.
- Use a level floor, or measure height from a level string line and correct for it.
- Measure to joint centers, not tube ends. Measure both sides and average them.
- CG height is the hardest input to know. A tilt-table or corner-weight measurement beats a guess, and anti-squat scales directly with it.
What the results mean
- Instant center (IC)
- Where the upper and lower link lines meet in side view. Under acceleration the axle pushes on the chassis as if through this one point. Parallel links put it infinitely far away.
- Anti-squat
- How much of the rear’s squat under acceleration the links resist. Draw a line from the rear tire contact patch through the IC to the front axle. Compare its height there with the CG height. The ratio is the anti-squat percentage. At 100% the rear neither squats nor rises. Above 100% it rises, and very high values can cause wheel hop. Below 100% it squats. The 4-link calculator uses the CG of the vehicle minus its rear unsprung weight, as the v3.0 spreadsheet does.
- Roll center and roll axis
- When the body rolls, the axle locates it about a line called the roll axis. The roll center is where that axis passes over the axle, given here as a height above the ground. A higher roll center means less body roll for a given spring setup, and more side-to-side jacking.
- For a 3-link, the axis runs from the Panhard bar’s midpoint to the point where the lower links cross the centerline. For a 4-link, it runs between the points where the upper links and the lower links each cross the centerline.
- Roll axis angle and roll steer
- The slope of the roll axis in side view. For a rear axle, an axis that slopes down toward the front gives roll understeer. One that slopes up gives roll oversteer. Zero means the axle doesn’t steer as the body rolls.
- Pinion angle change
- How much the axle housing rotates as it moves through travel. Positive means the pinion nose rotates up. Large changes affect driveshaft U-joint angles.
- Travel
- The calculators move the axle as one rigid piece. The lower links’ axle ends rise or fall by the travel amount and swing on their arcs, and the upper link ends follow. Anti-squat at each position is measured from the moved tire contact patch.
Link forces and tube strength
Link forces are found from the forward thrust the tires put into the axle: the vehicle weight times the thrust load factor, where 1 g means thrust equal to the vehicle weight. Each link group must balance that thrust and its turning moment about the tire contact patch. Positive force is tension, and negative is compression.
A 3-link’s single upper link usually sits off the vehicle centerline, so its pull also twists the axle about a vertical axis. The two lower links then carry different loads, and the Panhard bar takes the side load. The 3-link calculator solves this in 3D and shows both lower links and the Panhard bar’s force.
Each tube is then checked several ways, as in the spreadsheets:
- Yield: the tube’s cross-section stretching or crushing.
- Buckling: the Euler column load with pinned ends, for the same force reversed, as under braking.
- Bending: half the vehicle weight landing on the middle of the tube, as from a rock.
- Rod end: the joint’s rated load.
A factor of safety is capacity divided by load, so below 1 the part is predicted to fail under that load case. What margin is enough is your call. Real loads include impacts that a steady-state calculation doesn’t capture.
The materials come from the spreadsheets’ table, as typical published values. Certified mill data for your actual tube is better; enter it as a custom material.
Coilovers
The coilover calculator assumes a solid axle moving straight up and down, with the shock’s frame mount fixed. The shock keeps the same horizontal offset between its mounts and leans further as it compresses.
- Motion ratio
- Shock travel per inch of wheel travel. It equals the cosine of the shock’s angle from vertical, and it falls as the shock compresses.
- Wheel rate
- The spring rate felt at the wheel: spring rate × motion ratio², minus a small softening from the growing lean.
- Ride frequency
- How fast that corner bounces on its spring, in cycles per second. Softer setups have lower frequencies.
Gearing
Crawl ratio is first gear × transfer case low range × ring and pinion. Road speed is engine speed × tire circumference ÷ overall ratio. Speeds use the tire’s nominal diameter; a loaded tire rolls a few percent smaller.
The axle-shaft check is a first look, not a rating. It applies the torque one shaft could see to a solid round shaft at its smallest diameter, with shear yield taken as 0.577 × tensile yield. The torque is either all of the low-range torque through one shaft (a locked axle) or what one tire can push before it spins, whichever is less. Splines, heat treatment, fatigue and shock loads matter more than this.
Formulas
For a link with frame end F and axle end A, in side view:
slope m = (F.z − A.z) / (F.x − A.x) height at x = 0: b = A.z − m · A.x
Instant center, from the upper (U) and lower (L) link lines:
IC.x = (b_L − b_U) / (m_U − m_L) IC.z = m_U · IC.x + b_U
Anti-squat, with the contact patch at height g (0 at ride height):
AS% = ((IC.z − g) / IC.x) × (wheelbase / (CG − g)) × 100 parallel links: AS% = m × (wheelbase / (CG − g)) × 100
Link forces, with u the unit vector from axle end to frame end and T the thrust:
Σ Fx = 0: T + G_U · u_U.x + G_L · u_L.x = 0 Σ M = 0: G_U · (A_U.z · u_U.x − A_U.x · u_U.z) + G_L · (A_L.z · u_L.x − A_L.x · u_L.z) = 0 force per link = group force ÷ links in the group
Tube capacities, for outside diameter D, wall t, length L:
I = π/64 · (D⁴ − (D − 2t)⁴) A = π/4 · (D² − (D − 2t)²) P_yield = yield · A P_buckling = π² · E · I / L² P_bending = yield · I / (0.125 · D · L)
Coilover, with h the fixed horizontal offset between the shock mounts and L the shock length:
motion ratio MR = √(L² − h²) / L wheel rate = k · MR² − F_spring · h² / L³ ride frequency f = √(wheel rate · 386.09 / corner weight) / 2π
Where these calculators differ from the spreadsheets
The link geometry reproduces three spreadsheets: Dan Barcroft’s 3-link calculator v1.0, and the 4-link calculator v3.0 by Dan Barcroft and Greg Blanchette, plus its v3.1 travel edition revised by Chris Macock. The check runs 713 test cases (random layouts plus hand-picked edge cases) through the spreadsheets in Excel, and every value is compared. Anti-squat, instant center, roll axis, roll center, link lengths and tube capacities match to about a billionth. Five things differ on purpose:
- Link forces. Each spreadsheet formula balances moments for one link as if the other link took no part. The upper-link formula also adds a term that statics subtracts. Those shortcuts are exact for the spreadsheets’ own default layouts. In random layouts they were more than 5% off in about two of every three cases, and far off in some. These calculators solve the balance equations exactly. For the 3-link they also account for the off-center upper link, which loads one lower link more than the other: on the 3-link spreadsheet’s own defaults, the worse lower link carries 6.9% more than the spreadsheet’s average.
- Parallel links. Where links are parallel in side view, anti-squat comes from the link angle, which is the v3.0 spreadsheet’s own fix. The 3-link spreadsheet shows an error there.
- Travel. The v3.1 travel sheet moves the axle as a rigid four-bar linkage, and so do these calculators. For some link layouts the sheet’s angle construction jumps to the wrong solution. These calculators follow the linkage continuously from ride height, which was checked by stepping the linkage in small increments.
- Pinion angle. The travel sheet measures the axle’s angle with ATAN, so for some layouts it is off by 180° or divides by zero. These calculators measure the actual rotation, and positive means nose up.
- Undefined geometry shows a dash and a reason instead of a spreadsheet error. Examples are a vertical link, or a 4-link with both pairs parallel to the frame.
The coilover, crawl-ratio and axle-shaft calculations have no spreadsheet behind them. They are derived from the standard mechanics described above.