Bicycle gearshift (10; 110; 210) comprising - an articulated quadrilateral linkage with a base body and a mobile body connected together through a pair of connecting rods (13,15) articulated to the base body and to the mobile body, - a fixing group of the base body to a bicycle frame, - a chain guide mounted on the mobile body, the articulated quadrilateral linkage being associated with means for actuating the gearshift (50; 250) adapted for deforming the articulated quadrilateral linkage so as to determine a displacement of the mobile body with respect to the base body and consequently a primary displacement of the chain guide in the axial direction with respect to the axis of a cogset; wherein the fixing group comprises - a pin body, having an axis and intended for fixing the base body to the frame of the bicycle, - a mechanism for changing the relative angular position between the base body of the articulated quadrilateral linkage and the frame as a function of the primary displacement of the chain guide, wherein the mechanism for changing the relative angular position between the base body and the frame comprises: - a rotary body connected to the pin body such that a rotation of the rotary body determines a relative rotation about the axis between the pin body and the base body; - a pin (16; 116; 216) directly or indirectly set in rotation by the means for actuating the gearshift (50; 250), - a transmission (62, 63; 162, 163) between the pin (16; 116; 216) and the rotary body, characterized in that the transmission (62, 63; 162, 163) between the pin (16; 116; 216) and the rotary body has a variable gear ratio. - an articulated quadrilateral linkage with a base body and a mobile body connected together through a pair of connecting rods (13,15) articulated to the base body and to the mobile body, - a fixing group of the base body to a bicycle frame, - a chain guide mounted on the mobile body, the articulated quadrilateral linkage being associated with means for actuating the gearshift (50; 250) adapted for deforming the articulated quadrilateral linkage so as to determine a displacement of the mobile body with respect to the base body and consequently a primary displacement of the chain guide in the axial direction with respect to the axis of a cogset; - a pin body, having an axis and intended for fixing the base body to the frame of the bicycle, - a mechanism for changing the relative angular position between the base body of the articulated quadrilateral linkage and the frame as a function of the primary displacement of the chain guide, wherein the mechanism for changing the relative angular position between the base body and the frame comprises: - a rotary body connected to the pin body such that a rotation of the rotary body determines a relative rotation about the axis between the pin body and the base body; - a pin (16; 116; 216) directly or indirectly set in rotation by the means for actuating the gearshift (50; 250), - a transmission (62, 63; 162, 163) between the pin (16; 116; 216) and the rotary body, - a rotary body connected to the pin body such that a rotation of the rotary body determines a relative rotation about the axis between the pin body and the base body; - a pin (16; 116; 216) directly or indirectly set in rotation by the means for actuating the gearshift (50; 250), - a transmission (62, 63; 162, 163) between the pin (16; 116; 216) and the rotary body,