Motion ratio explained
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 wheel rate is the spring rate divided by the motion ratio squared.
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 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.
How to decide the motion ratio?
It basically depends on 3 factors
a)Bending Moment: To reduce the bending moment the strut point should be near to the wheel.
b)Suspension Stiffness: The suspension tends to get stiff when its inclination of the shock absorber to horizontal tends to 90 deg.
c)Half Shafts: In Rear suspension the wheel travel is constrained by the angle limitations of 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.