CHAPTER 1 INTRODUCTION
1.4 T HESIS O UTLINES
In order to develop a model including all factors affecting the optimal cadence, the cycling model and factor analysis have be done in this thesis. And the model can help to determine how to choose a suitable gear ratio. The brief description of outlines on this thesis contents are given as follows.
Chapter 2 is the preliminary details which include brief introduction about lower limb in anatomy and some terminology on the bicycle. Chapter 3 introduces that the factors influence human cycling and the effect of this factors about rider’s performance. Chapter 4 proposes the basic concept and detail design steps for fuzzy logic controller. And the fuzzy logic controller of the gear-shifting is designed in Chapter 4. In Chapter 5, this study constructs the experiments machines by combing the software and hardware. And it has discussion about test results and compare to the Browning SmartShift system. Finally, Chapter 6 contains the conclusions and future works, which could assist some aspects for following works on this study.
CHAPTER 2
PRELIMINARY DETAILS
2.1 Lower limb in Anatomy
Human beings use their lower limb to ride a bicycle. But lower limb have complex constructions. In order to make it easy understanding, its structure can be divided into three groups. This section will introduce the lower limb constructions by the anatomy point of view.
2.1.1
BonesThe lower limb carries the entire weight of the stand body, and is subjected to exceptional forces when people jump or run. Thus, it is not surprising that the bones of the lower limbs are thicker and stronger than the comparable bones of the upper limbs. The three segments of the free lower limb are the thigh, the leg, and the foot. As shown in Fig 2.1, the main bone of the thigh is femur. The head of the femur is the ball that articulates with the acetabulum. This head is mounted on a neck, a projection from the femur. Two ridges extend from the femur for the attachment of muscles. The main bones of the leg are tibia and fibula.
The distal region of the leg is supported by the tibia and fibula. The tibia is the larger of these two; it directly articulates with the femur. The fibula articulates the tibia at its proximal end.
The main bones of the foot are tarsal, metatarsals and phalanges. The tarsal bones directly articulate with tibia and fibula. Metatarsals extend the length of the foot. The toes contain phalanges, just as the fingers do.
Fig 2.1 The bones of lower limb [9]
2.1.2
MusclesThere are lots of muscles at the lower limb. Introducing these muscles from hip to ankle can make it easy to understand. There are two directional terms: anterior and posterior.
Anterior means toward the front of the body, and posterior means toward the back of the body.
The anterior muscles that move the thigh at the hip all function to flex and laterally rotate the hip. The posterior muscles extend, abduct, and some medially rotate the hip. That detail information are showed in Table 2.1. The medial muscles that move the thigh at the hip have all functions to adduct the thigh, as shown in Table 2.2.
Table 2.1 The muscles that move the thigh at the hip [10]
Origin Insertion
Iliacus iliac fossa lesser trochanter of femur
Psoas major transverse process of lumbar vertebrae lesser trochanter of femur Gluteus
maximus
iliac crest, sacrum, coccyx, aponeurosis of lumbar region
gluteal tuberosity and iliotibial tract Gluteus
medius lateral surface of ilium greater trochanter of femur Gluteus
minimus lateral surface of ilium greater trochanter of femur
Muscle
tensor fasciae
latae anterior border of ilium and iliac crest iliotibial tract
Table 2.2 The medial muscles that move the thigh at the hip[10]
Origin Insertion
Gracilis symphysis pubis proximomedial surface of tibia Pectineus pectineal line of pubis distal to lesser trochanter of femur Adductor
longus pubis linea aspera
Adductor brevis pubis linea aspera
Muscle
Adductor magnus
inferior rami of pubis and ischium
linea aspera and medial epicondyle of femur
The muscles of the thigh that move the leg are divided into an anterior group and a posterior group. The primarily function of the anterior group is to extend the leg at the knee, and the function of the posterior group is to extend the thigh at the hip and flex the leg at the knee, as shown in Table 2.3.
Table 2.3 The muscles of the thigh that move the leg [10]
Origin Insertion
Sartorius anterior superior iliac spine medial surface of tibia Rectus femoris anterior superior iliac spine patella by common tendon Vastus lateralis greater trochanter and linea
aspera patella by common tendon Vastus medialis medial surface and linea aspera patella by common tendon
Vastus intermedius
anterior and lateral surfaces of
femur patella by common tendon
Biceps femoris ischial tuberosity; linea aspera head of fibula and lateral epicondyle tibia
Semitendinosus ischial tuberosity proximal portion of shaft of tibia
Muscle
Semimemebranos
us ischial tuberosity medial epicondyle of tibia
The muscles of the leg that move the ankle, foot, and toes are separated into an anterior group (including tibialis anterior) that dorsiflexes the foot and extends the digits, a lateral group (the peroneal muscles) that aid in dorsiflexion and eversion, and a posterior group (including gastrocnemius and soleus ) that plantar flexes the foot and flexes the toes. The descriptions are shown in Table 2.4.
Table 2.4 The muscles of the leg that move the ankle [10]
Origin Insertion
Tibialis anterior lateral condyle of tibia 1st metatarsal and tarsal Gastrocneumius lateral and medial epicondyle of femur posterior surface of calcaneus
Muscle
Soleus posterior aspect of fibula and tibia calcaneus
Several muscles shown in Fig 2.2 and 2.3, are the main power source when riding bicycles. Rectus femoris is the superficical muscle of the anterior thigh and the longest head, and it is the only muscle in the group crossing the hip point. It runs straight down the thigh.
The Vastus lateralis forms lateral aspect of the thigh. It is a common intramuscular injection site, particularly in infants. Vastus medialis forms inferomedial aspect of thigh. Vastus intermedius is obscured by rectus femoris. It lies between vastus lateralis and vastus medialis on the anterior thigh. Gluteus maximus is the largest and most superficial of gluteus muscles.
It forms bulk of the buttock mass. Its fibers are thick and coarse. It overlies the large sciatic nerve and covers the ischial tuberosity only when standing. When sitting, it moves superiorly leaving the ischial tuberosity exposed in the subcutaneous position. The Biceps femoris is lateral muscles of the posterior group and arises from two heads. The Tibialis anterior is superficial muscles of the anterior leg, and laterally paralles sharp anterior margin of the tibia.
Gastrocnemius are superficial muscles of pair.
Fig 2.3 Lower limb muscles posterior [9]
2.1.3
JointsThere are three joints in the lower limb that is important during cycling. These three joints are hip joint, knee joint and ankle joint. All of these joints are synovial joints. The synovial joints are the most moveable joints of the body, and all are diarthroses. Each synovial joint contains a fluid filled joint cavity. Most joints of the body are synovial joints, especially those in the limbs. The hip joint articulates with coxal bone and femur. Its structural type is ball and socket of synovial joint. Its functions types are multiaxial, flexion, extension, abduction, adduction, rotation and circumduction. The knee joint includes tibiofemoral segment and femoropatellar segment. The structural types of these two segments are hinge of synovial joint and gliding of synovial joint. The function types of the tibiofemoral segment are uniaxial, flexion, extension and some rotation. The function type of the femoropatelar segment is gliding. The ankle joint articulates tibia and fibula with talus. Its structural type is hinge of the synovial joint. Its function type is uniaxial, flexion and extension.
2.2 Definitions of terms
In this section, some concepts related to bicycle science will be presented. Some terminology used is introduced as follows:
1. Pedal forces:
The feet generate forces acting on the pedals. The forces are usually between horizontal and vertical directions.
2. Muscle stress:
Stress is used to describe the distribution of a force over the area on which it acts. It is expressed as force intensity, that is, forces per unit area.
Area Force Stress=
(1) Muscle architecture is typically described in terms of muscle length, mass, myofiber length, pennation angle, and physiological cross-section area (PCSA). PCSA is an approximation of the total cross-section area of all muscle fibers, projected along the muscle’s line of action. It is calculated as:
(mm) surface pennation angle, and Lf is the myofiber length [11]. Therefore, use the pedal force divide by PCSA can obtain the muscle stress.
3. Joint moment:
The moment of a force about a point is the vector product of the force and the distance:
d where d represents the perpendicular distance from the point to the line of action of the force. Therefore, the moments from pedal forces act on hip, knee and ankle can be computed by the formula .
4. Human power:
The capacity of a machine can be measured by the time rate at which it can do works or deliver energies. The power P developed by a force F which does an amount of work U is Therefore, the power generated by human forces to make bicycle to go forward can be computed by this formula.
5. Torque:
The component of the moment about the rotating axis of the subject is called the torque.
The pedal forces act on the pedal and generate torques on the pedal axis.
6. Gear-ratio:
It means front chainring teeth divided by rear chainring teeth.
7. Down-shifting:
The chain is shifted from a larger chainring to a smaller chainring in the front derailleur system, or from a smaller chainring to a larger chainring in the rear derailleur. A smaller gear-ratio can be obtained.
8. Up-shifting:
It is the reverse of down-shifting. A larger gear-ratio can be obtained.
9. EMG:
The technique of recording the electrical activity produced by the muscle, or the myoelectric activity, is known as the electromyography (EMG). Electrodes placed on the
CHAPTER 3
CYCLING PERFORMANCE FOR HUMAN
3.1 Forces
Riders generate pedaling forces to make bicycles moving forward. If more forces are generated, the bicycles will go faster. At the same time, forces make people to generate joint moments and muscle stresses. These two factors make rider feel tired or even injure rider’s body.
In 1985, M. L. Hull and M. Jorge measured normal and tangential pedal forces and joint moment [12]. They made a model to perform some detailed biomechanics analysis of the lower limb. In 1986, Rob Redfield and M. L. Hull made an experiment to test the relation between joint moments and pedaling rates at a constant power during cycling [2]. They used a five-bar linkage model to simulate the bicycle rider system as shown in Fig 3.1. They defined the optimal cadence which minimizes the sum of the average of the absolute hip and knee moments. As shown in Fig 3.2, they found that the cadence minimizes the hip moment of 12 N-m at 95 rpm and the knee moment of 17 N-m at 105 rpm. So they decided the optimal cadence is 90 to 105 rpm. They also made another experiment to minimize the two cost functions [3]. One is based on joint moments and the other is based on muscle stresses. Both cost functions offer reasonable predictions of pedal forces. But the muscle stresses cost function predicts better than joint moments as shown in Fig 3.3 and 3.4. Because the cost function of muscle stresses predicts hip moments that compare favorable with the actual hip moment.
Fig 3.1 Five-bar linkage model [2]
Fig 3.3 Hip moment comparison (moment case) [3]
Fig 3.4 Hip moment comparison (stress case) [3]
In 1988, Hull, M. L. et al. [4] found the optimal pedaling rate using a muscle stress based objective function. They avoided redundant equations and computed stresses in 12 lower limb muscles. They also measured the stresses in muscles crossing the joint, but they thought it is less important than stresses in muscles at thigh and leg. As shown in Fig 3.5, the optimal pedaling rate falls in the range of 95 to 100 rpm. Its result agreed with the range founded by Rob and Hull in 1986 [4].
Fig 3.5 Muscle stress cost function [4]
In 1999, Neptune and Herzog [13] made experiments about pedaling forces and pedaling rates. As shown in Fig 3.6 the components of average resultant muscular and non-muscular pedaling force systematically decreased and increased respectively as pedaling rates increased. The total average resultant pedaling force varies with pedaling rate to reach a minimum value at 90 rpm.
Fig 3.6 Average muscular and non-muscular pedal forces [13].
In 1999, Neptune and Hull [6] made an analysis and simulation of preferred cadence selection. They investigated neuromuscular quantities such as the individual muscle forces, stress and endurance. The results from these pedaling simulations indicated that all neuromuscular quantities are minimized at 90 rpm when summed across muscles, as shown in Fig 3.7.
Fig 3.7 Normalized neuromuscular quantities across the different pedaling rates [6]
In 2000, Marsh, et al. [5] made an experiment about relationship between joint moment and preferred pedaling cadence. They defined a joint moment based cost function that is the sum of the average absolute joint moments at the hip, knee and ankle. They divided three groups of cyclists: trained cyclists, runners and less-trained cyclists. As shown in Fig 3.8, the cost function cadence increased as power output increased. In addition, the increases are similar for all three subject groups. In the three group, the cost function cadence is significantly higher at 150 W (93.3±10.4rpm) than at 100 W (86.3±11.9rpm). For the trained cyclists and runners groups, the cost function cadence increases from 86.3±10.2 to
6 . 9 0 .
94 ± rpm and again to 98.5±8.0 rpm and decreases slightly to 96.1±7.3 rpm as power output increases from 100 to 250 W. The cost function cadences of trained cyclists,
power output increased. The cost function cadence at 200 W for cyclists and runners (101 and 96 rpm) agreed closely with previous research by Redfield and Hull who reported a cadence in the range of 90 to 105 rpm.
In summary, the conclusions from previous studies about the optimum cadence are:
1. Minimizing the joint moments can get the optimal pedal cadence ranges between 90 to 105 rpm.
2. Minimizing the muscle stress can get the optimal pedal cadence ranges between 95 to 100 rpm.
3. Minimizing the pedal force can get the optimal pedal cadence about 90 rpm.
4. The experience of riders influence the results a lot in human cycling.
Fig 3.8 Influence of cadence and power output on the moment based cost function [5]
Fig 3.9 Mean preferred and cost function cadences for trained cyclist and runners [5]
Fig 3.10 Mean preferred and cost function cadences for less-trained cyclist [5]
3.2 Cardiovascular
The cardiovascular system is an important factor when riding a bicycle. People riding bicycles will pant and his heartbeat become fast. It will make riders feel tired and uncomfortable. If a rider’s cardiovascular system can endure the loading from cycling, he or she can ride for a long time. Wilson [7] indicated that everyone should be able to work easily at one-third of maximal oxygen uptake, but exceeding two-thirds of maximal oxygen uptake for a long duration may require considerable training. For a non-trained person, the maximum oxygen-absorption rate (VO2 max) is assumed to be about 50 ml/s. When a rider is using about a third of his maximum oxygen-absorption rate, the power output is about 0.1 hp (75W).
He thought that common people can work under these conditions for several hours without suffering fatigue.
In 1981, Hagberg et al. [15] made experiments to find the effect of pedaling rate on submaximal exercise responses of competitive cyclists. The road-racing cyclists used gears during the loaded cycling trials that elicited pedal cadences between 68 and 126 rpm. They measured rider’s heart rate, oxygen consumption, expiratory flow, and blood lactate. And the heart rate increase, whereas net heart rate (after subtracting the heart rate during unloaded cycling) decreased with increasing pedal rate during loaded cycling. Expiratory flow, oxygen consumption and blood lactate increased much more rapidly above the optimal cadence than blow it. They found that the optimal cadence for each subject ranged from 72 to 102 rpm.
In 1993, Marsh and Martin made experiments to compare the preferred cadences and the
They found that the preferred cadence was significantly higher than the most economical cadence for both cyclists and non-cyclists, and higher cadences produce higher oxygen consumption. Both cyclists and non-cyclists reported that they felt more comfortable at the higher cadences during 200 W cycling. And both preferred cadence and the most economical cadence of cyclists are lower than non-cyclists’. In 1999, Woolford [14] and his coworkers made experiments and found that for the same power output, maximum oxygen consumption is smaller at pedal cadences of 90~100 rpm compared with 120~130 rpm. The results here can be concluded as:
1. Riding bicycles emphasize the strength in legs more than the cardiovascular system.
2. Higher cadences make rider comfortable and can ride for a long time, but it cost more oxygen consumption.
3. Cyclists have a stronger cardiovascular system than non-cyclists, so they can use less oxygen consumption at the same cadence.
Fig 3.11 Cadence and oxygen consumption [8]
3.3 Power and torque
If a rider can maintain higher power, he or she can ride bicycle more easily. High power means using energy well. It makes riders easy to move bicycles forward. Riders generate force to make torque on the shaft of the pedals. Lower cadence leads high torque. High torque means that high angular acceleration and high pedaling forces generated. High angular acceleration can make rider get the high velocity in a short time, but high pedaling forces might break rider’s body. On the contrary, high cadence generates lower torque, and it might make rider easy to feel tired.
One experiment was made to test the relationship between power output and pedal cadence [16]. As shown in Fig 3.12, the subject developed maximum power for all duration at 40 to 50 rpm and the maximum muscle efficiency was achieved at about 50 rpm. And another experiment used to find the power output an ordinary untrained cyclist could maintain over useful periods of time. The results showe in Fig 3.13, for prolonged periods about 0.05 hp was maintained with pedaling rates of 20 to 60 rpm.
Fig 3.13 Relationship of pedaling speed to torque [16]
In 1997, Martin [17] and his coworkers demonstrated that instantaneous cycling power-velocity and torque-velocity relationships across a range of pedaling rates from a single exercise. They measured the instantaneous power (PI ) and computed the average power (PREV). As Fig 3.14 and Fig 3.15 shown, maximum value of PREV is 1317±66W and can be achieved at a pedaling rate of 122± rpm. Maximum value of 2 PI averaged is
101
2137± W and occurres at a pedaling rate of 131±2 rpm. They also measured the instantaneous torque (TI) and computed the average torque (TREV) as Fig 3.16 shown. The result matches with Fig 3.17 reported by Wilson [7]. He indicated that some people produce maximum power at 120 rpm and can spin up to 180 rpm, whereas others can manage only half these speeds. These results can be concluded as:
1. High pedaling cadence is not totally good for human power.
2. The relationship between human power and torque conforms to the theory.
2. The relationship between human power and torque conforms to the theory.