Motion ratio

Key takeaways

Motion ratio belongs to engineering; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Motion ratio to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Motion ratio from memory before moving on to harder problems.

Reference excerpt

The motion ratio of a mechanism is the ratio of the displacement of the point of interest to that of another point. The most common example is in a vehicle's suspension, where it is used to describe the displacement and forces in the springs and shock absorbers. The force in the spring is (roughly) the vertical force at the contact patch divided by the motion ratio, and the spring rate is the wheel rate divided by the motion ratio squared.

I R = S p r i n g D i s p l a c e m e n t W h e e l D i s p l a c e m e n t . {\displaystyle IR={\frac {SpringDisplacement}{WheelDisplacement}}.}

M R = W h e e l D i s p l a c e m e n t S p r i n g D i s p l a c e m e n t . {\displaystyle MR={\frac {WheelDisplacement}{SpringDisplacement}}.}

W h e e l r a t e = S p r i n g r a t e ∗ I R 2 . {\displaystyle Wheelrate={Springrate}*{IR^{2}}.}

W h e e l r a t e = S p r i n g r a t e / M R 2 . {\displaystyle Wheelrate={Springrate}/{MR^{2}}.}

This is described as the Installation Ratio in the reference. Motion ratio is the more common term in the industry, but sometimes is used to mean the inverse of the above definition. Motion ratio in suspension of a vehicle describes the amount of shock travel for a given amount of wheel travel. Mathematically, it is the ratio of shock travel and wheel travel. The amount of force transmitted to the vehicle chassis reduces with increase in motion ratio. A motion ratio close to one is desired in the vehicle for better ride and comfort. One should know the desired wheel travel of the vehicle before calculating motion ratio, which depends much on the type of track the vehicle will run upon. Selecting the appropriate ratio depends on multiple factors:

Bending moment: To reduce the bending moment the strut point should be close to the wheel. Suspension stiffness: Suspensions tends to stiffen when the inclination of the shock absorber to horizontal tends to 90 degrees. Half-shafts: In suspensions of driven wheels, wheel travel is in many cases constrained by the universal joints of the half shafts. Design the motion ratio such that at maximum bounce and rebound shocks are the first components that bottom out by hitting bump stops.

References Milliken, William F.; Milliken, Douglas L. Race Car Vehicle Dynamics. SAE International. ISBN 978-1-56091-526-3. Smith, Carroll (June 1978). Tune To Win. SAE International. ISBN 978-0-87938-071-7. Suspension Geometry Calculator

Worked examples

Example 1 — a first encounter with Motion ratio

Start with the simplest possible case. Write down what Motion ratio claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In engineering, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Motion ratio before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Motion ratio ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Motion ratio

In research: Motion ratio appears in engineering research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Motion ratio in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Motion ratio is common in secondary-school and first-year university syllabi. It links to neighbouring topics Automotive suspension technologies, Automotive technology stubs, Engineering ratios, so understanding it makes those chapters shorter.
In everyday life: Look for Motion ratio outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

How to study Motion ratio in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Motion ratio means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Motion ratio out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Motion ratio in simple terms?

The motion ratio of a mechanism is the ratio of the displacement of the point of interest to that of another point. The most common example is in a vehicle's suspension, where it is used to describe the displacement and forces in the springs and shock absorbers.

Why does Motion ratio matter?

Because it connects several engineering ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Motion ratio?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Motion ratio.