# A Novel Gear-shifting Strategy Used on Smart Bicycles

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3 social sciences, eliminating the difference in the approaches between natural and social sciences. The fuzzy logic controller is a tool for processing a fuzzy form of information in a non-fuzzy or fuzzy scheme of reasoning. As shown in Fig. 1, a simple fuzzy logic controller contains a fuzzification interface, a fuzzy knowledge base, an inference engine, and a defuzzification interface. Fig. 1: The fuzzy logic controller (a basic structure) According to literature reviews, this study chooses the pedal cadence range to construct the fuzzy set. Riders can feel comfortable riding in this range because it costs small loading of forces, muscle stress, joint moment, neuromuscular, and VO2. This study uses two input variables, velocity (v) and pedal cadence (u), and one output variable, gear-ratio (g). The membership functions are shown in Fig. 2. (a) membership function of velocity (v) (b) membership function of pedal cadence (u) (c) membership function of gear-ratio (g) Fig. 2: membership functions of input and output variables 43

4 There are two inputs and one output variables, nine fuzzy rules can be constructed as shown in Table 1. The general form of the rules in this case of two-input-single-output system is: Rule i : IF (v is V i ) AND (u is U i ), THEN (g is G i ), i=1 to 9. where v, u and g are linguistic variables representing the velocity, pedal cadence and gear ratio, respectively. V i, U i and G i are the linguistic values of the variables v, u and g. Take the rule 3 in Table 1 for an example, if the input velocity is slow and pedal cadence is fast, it means that the gear ratio is small at the moment, and the pedal cadence is too fast. Therefore, the output gear ratio should be change to a medium one in order to lower the pedal cadence and increase the velocity. Rule # Table 4.1 Fuzzy rule base IF THEN Velocity (v) Pedal cadence (u) Gear-ratio (g) 1 Slow Slow Very Small 2 Slow Medium Small 3 Slow Fast Medium 4 Medium Slow Small 5 Medium Medium Medium 6 Medium Fast Big 7 Fast Slow Medium 8 Fast Medium Big 9 Fast Fast Very Big This study used the max-min composition as the inference method. It is the most famous one and suitable for all situations. Since the fuzzy rule base consists of compositional relations of inference: R=(V P) G, the max-min composition is used as the fuzzy implication. Take the nine rules in Table 1 for example, the IF side is taken the AND (MIN) operation as shown in the following equations: μg ( g) = μ ( v) ( u) i V μ, i=1 to 9 (1) i U i And the final inferred consequent G according to the OR (MAX) operation is shown in the following equations: μg ( g) = μg ( g) μg ( g) μg ( g)... μg ( g) (2) Finally, the center of area (COA) method is selected as the defuzzification strategy. The operation is shown in the following equation: g μg( g) gdg * g = μ ( g) dg g G This method determines the center of area (g * ) below the combined membership function. The center of area means the desired gear ratio. It can be compared to the current one. If the desired gear-ratio is larger, it means the fuzzy logic controller suggests a larger gear-ratio than the current one. Therefore, a up-shifting command must act on the derailleur system to obtain a larger gear-ratio. 4. Experimental Results In order to implement the proposed fuzzy logic controller, a Browning 12-speed SmartShift bicycle (Fig.3) with an 8051 based control architecture is used for the hardware. The fuzzy logic controller is implemented in the ECU (Electrical Control Unit) box. (3) 44

6 5. Discussions and Conclusions Based on the experimental results, it is obvious that the fuzzy logic controller works well to improve the gear-shifting performance during riding bicycles. The controller changes gears depending on the velocity and the pedaling cadence. The results show that it can change gears not only matching the physical environments but also taking care of the riders. Therefore, it changes gears more stable and correct. And it changes not so frequently that can make riders easy to operate the bicycle and feel more comfortable. The pedaling cadence range of the different riders is from 60 to 85 rpm. There are many factors influencing the riders performances. But the point is that if the riders know how to choose the gear-ratio and ride at the optimal cadence, then he or she can get the best performances or most comfortable feelings. In this study, the new shifting strategy is completed by fuzzy logic control theory. And it was implementing using the Browning SmartShift system. It can test and get experiment data after combining the software and hardware. Integrating the fuzzy logic controller with the optimal gear-shifting sequence make the strategy more complete. The optimal gear-shifting sequence can decrease power lose during gear-shifting 6. References [1] Redfield, R. and Hull, M. L., On the relation between joint moments and pedaling rates at constant power in bicycling, Journal of Biomechanics, Vol. 19, No. 4, pp , [2] Redfield, R. and Hull, M. L., Prediction of pedal forces in bicycling using optimization methods, Journal of Biomechanics, Vol. 19, No 7, pp , [3] Hull, M. L., Gonzalez, H. K. and Rob Redfield, Optimization of pedaling rate in cycling using a muscle stressbased objective function, International Journal of Sport Biomechanics, Vol. 9, pp. 1-20, [4] Marsh, A.P., Martin, P.E., and Sanderson, D. J., Is a joint moment-based cost function associated with preferred cycling cadence, Journal of Biomechanics, Vol. 33, pp , [5] Neptune, R. R. and Hull, M. L., A theoretical analysis of preferred pedaling rate selection in endurance cycling, Journal of Biomechanics, Vol. 32, pp , [6] Wilson, D. G.., Bicycling Science, 3 rd, MIT Press, Cambridge, MA, [7] Marsh, A.P. and Martin, P.E., The association between cycling experience and preferred and most economical cadences, Medicine and Science in Sports and Exercise, Vol. 25, No. 11, pp , [8] Zadeh, L., Fuzzy sets, Inf. Control, Vol.8, pp ,

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