Rear Suspension Linkage Motion Study and Wheel Travel

The problem

A linkage between swingarm and shock lets designers shape how stiff the suspension feels through its travel. Electric motorcycles carry a heavy battery and often a different mass distribution, so a copied linkage may not suit them. Students need a way to see how link lengths and pivot positions change leverage ratio and to size the spring accordingly.

Objectives

• Lay out a swingarm, rocker, pull rod and shock with pivot points as parameters.
• Run a Motion study to plot shock stroke, leverage ratio and wheel rate against wheel travel.
• Tune geometry for a chosen rate curve and size the spring for an example load.
• Extract pivot loads for a later strength check of the links.

What you need

Key concepts

Leverage ratio

Wheel travel divided by shock travel at a point in the stroke. A falling leverage ratio through travel gives a rising (progressive) wheel rate.

Wheel rate

The effective spring stiffness felt at the wheel, roughly spring rate divided by leverage ratio squared, which sets ride feel and sag.

Sag

How far the suspension compresses under the static weight of bike and rider, usually set as a fraction of total travel.

Instantaneous kinematics

At each wheel position the links have a particular geometry; a motion study steps through positions to compute ratios and forces.

Step-by-step guide

1. 1

   Set requirements

   Define an example electric motorcycle: rear wheel travel 120 mm, rear static load from bike and an example 80 kg rider, target static sag around 30 per cent of travel and a progressive rate with an example 20 to 30 per cent rise in leverage from top to bottom. Note packaging limits: the battery and motor occupy the space under the seat, so the shock and rocker must fit around them. Record a shock size from a catalogue as an envelope.

   Checkpoint: A requirements table with travel, loads, sag target, progression target and packaging envelope.

2. 2

   Lay out the linkage in 2D

   In a Layout sketch, draw the swingarm pivot, wheel axle, rocker pivots, pull rod and shock mounts as lines and points. Turn each link into a block with Make Block, then constrain the blocks with coincident relations at pivots so they can move. Drag the axle through its travel and read shock length at several positions using dimensions. This quick check lets you try many geometries before modelling solids.

   Checkpoint: A layout where dragging the axle moves the linkage correctly and shock length changes smoothly.

3. 3

   Tune the layout

   Move the rocker and pull rod pivots and note the shock length at top, sag and bottom positions. Compute leverage ratio at each step in a spreadsheet. Adjust until the ratio falls through travel by your progression target, without any link passing through a straight-line toggle position. Keep the shock within its stroke with a margin at both ends. Save each trial as a separate layout configuration so you can compare curves later.

   Checkpoint: A layout where leverage ratio falls smoothly through travel and the shock stays within its stroke.

4. 4

   Model parts from the layout

   Create parts in context from the layout blocks: swingarm, rocker plates, pull rod, and simple shock body and shaft parts. Use an aluminium or steel from the material library and realistic sections. Add bearing bores at pivots. Keep pivot locations linked to the layout so changes flow through, or break the links deliberately once the geometry is frozen and record that.

   Checkpoint: Solid parts whose pivot positions match the layout within 0.1 mm.

5. 5

   Assemble with mates

   Fix the frame. Add concentric mates at every pivot and coincident or width mates to centre links. Mate the shock body and shaft with a concentric mate and limit the shaft travel with a limit distance mate. Check the assembly moves through full travel when dragging the wheel, and that degrees of freedom are what you expect: one for the whole linkage.

   Checkpoint: Dragging the wheel moves the whole linkage through travel with no over-defined mates or errors.

6. 6

   Set up the Motion study

   Create a Motion study and choose Motion Analysis. Add a linear motor at the axle, driving it vertically by displacement from top-out to full bump over a set time. Add a linear spring between the shock mounts with an initial rate and free length, and an optional damper. Turn on gravity. Without Motion Analysis, use Basic Motion with a motor and measure shock length in a sketch, accepting that forces will not be computed.

   Checkpoint: The study runs and the animation shows the linkage moving through full travel.

7. 7

   Plot and export results

   Create Results and Plots for axle vertical displacement, shock length (distance between mount points) and spring force. Export the data to CSV. In Excel, compute leverage ratio as the derivative of wheel travel with respect to shock travel, and wheel rate as spring rate divided by leverage ratio squared. Plot both against wheel travel. Compare with the layout estimate. Use a fine enough frame rate in the study that the derivative is smooth rather than stepped.

   Checkpoint: Leverage ratio and wheel rate curves that agree with the layout estimate within a few per cent.

8. 8

   Size the spring and check sag

   With the example static load at the wheel, find the wheel travel where wheel force equals load for a trial spring rate, accounting for preload. Iterate the spring rate until sag meets the target. Check the force at full bump against the bump stop and shock rating. Report the chosen spring rate, preload and sag. Repeat the check with rider only and with rider plus a passenger or luggage, so sag stays acceptable across the load range.

   Checkpoint: A spring rate and preload that give the target sag, with full-bump force within the shock rating.

9. 9

   Extract pivot loads and check a link

   Plot reaction forces at each pivot through travel, and find the worst case, often at full bump. Use the Import Motion Loads option in SOLIDWORKS Simulation if your licence includes it, or apply the forces manually in a static study of the rocker with bearing bore fixtures. Check stress against the material yield and the factor of safety against a target.

   Checkpoint: Rocker factor of safety above an example 2 at the worst-case load.

10. 10

    Drawings and report

    Make drawings of the rocker and pull rod with pivot positions and bore tolerances, using GD&T for bore position relative to each other. Write up requirements, layout tuning, motion results, spring sizing and link check. State limitations: rigid links, no tyre deflection, quasi-static motion. Suggest measuring sag on a prototype to validate the spring choice. Include a bearing or bush callout at each pivot and a material and finish note on every drawing.

    Checkpoint: Drawings with toleranced pivots and a report with leverage, wheel rate and spring sizing curves.

Testing & validation

• Leverage ratio from the Motion study matches the 2D layout check.
• Wheel rate curve shows the intended progression.
• Calculated sag meets the target with the chosen spring.
• Rocker strength check meets the factor-of-safety target under the worst pivot load.

Expected results

A tuned rear linkage with leverage ratio and wheel rate curves, a sized spring and preload, pivot loads through travel and a strength-checked rocker with drawings.

Take it further

• Add a drive force line and study anti-squat for a belt or chain drive.
• Compare a direct-mount shock with the linkage on rate progression.
• Run a fatigue study on the rocker with a load spectrum.
• Build a 3D-printed scale model to demonstrate the linkage.

Viva and review questions

Learn it at DIYguru

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