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1. An auxiliary device for a bicycle wherein the bicycle includes a bicycle frame, two treadles, two cranks, a freewheel axle, a chain wheel, a chain, a rear-wheel axle, and the auxiliary device comprises:
a pair of thrusting members positioned at two sides of the bicycle near a seat of the bicycle in a one-up-one-down manner; and a drive mechanism being pivotally coupled between the thrusting members and the bicycle and comprising: two first pivots, a second pivot and a linkage system, wherein the first pivots and the second pivot are pivotally coupled with the linkage system, respectively, and the linkage system has at least one end pivotally coupled with the first pivots and an opposite end pivotally coupled with components of the bicycle nearby travels of the cyclist's downward moving thighs and shanks; whereby, when the cyclist has back thigh muscles thereof pressing the thrusting members and treadles of the bicycle, the linkage system in response to the downward pressing force from the cyclist's thighs and shanks makes the thrusting members move up or down synchronously, so as to reduce burden bore by the cyclist's back thigh muscles and shank muscles, and enhance the cyclist's riding speed and endurance.
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