brake shoe 44b is attached to shoe attachment portion 42b such that brake shoe 44b can be adjusted vertically to ensure proper engagement between brake shoe 44b and rim 18 of bicycle wheel 19 brake shoe 44b has a shoe fastening pin not seen in the figs a shoe holder 122b which is fastened to the tip end of the shoe fastening pin a nut 124b threadedly coupled to the free end of the shoe fastening pin and a friction pad 126b constructed of a suitable friction material which is attached to the shoe holder 122b as seen in fig2 link member 43a as seen in fig4 6 has a somewhat u shaped cross section with a pair of connecting portions 130a connected together by a central portion 132a each of the connecting portions 130a has a hole 134a in its lower end and a hole 136a in its upper end for receiving the pins 64a and 119a respectively to couple mounting member 38a to brake shoe attachment portion 42a more specifically the first pin 64a is used to couple the lower end of link member 43a to mounting member 38a pin 119a is used to couple the upper end of control link member 43a to brake attachment portion 42a link member 43a together with brake arm 40a brake shoe attachment portion 42a and mounting member 48a forms a parallel push mechanism in the form of a parallelogram such that the brake shoe 44a moves in a substantially straight movement to engage the rim.