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In recent years, higher performance of motorcycles has been attained through improvements in engine performance and rigidity of frames etc., and there is now increasing demand for a more efficient suspension which gives better ride and handling stability. In many of the conventional motorcycles, the rear suspension supported the rear body on both sides of the rear wheel by means of two suspension units. However, such two-unit-type suspension is presently being replaced by a single-unit-type suspension called a “mono shock” which is mounted on the central part of the body with a view to concentrating the body mass and also to lowering the gravity center of the motorcycle. Such change in the mounting location of the suspension unit greatly affects the operation of the suspension unit. For example, the ratio of displacement of the suspension unit to that of the axle is reduced to 0.3 - 0.5 from the previous ratio of about 1.