Download pdf - Power output and work in different muscle groups during ergometer cycling

Eur J Appl Physiol (1986) 55:229--235 European Journal of

Applied Physiology and Occupational Physiology �9 Springer-Verlag 1986

Power output and work in different muscle groups during ergometer cycling

Mats O. Ericson, ~,ke Bratt, Ralph Nisell, Ulf P. Arborelius, and Jan Ekholm

Kinesiology Research Group, Department of Physical Medicine & Rehabilitation and Department of Anatomy, Karolinska Institute, and Department of Mechanics, Royal Institute of Technology, Stockholm, Sweden

Summary. The aim of this study was to calculate the magnitude of the instantaneous muscular power output at the hip, knee and ankle joints during ergometer cycling. Six healthy subjects pedalled a weight-braked bicycle ergometer at 120 watts (W) and 60 revolutions per minute (rpm). The subjects were filmed with a cine camera, and pedal reaction forces were recorded from a force transducer mounted in the pedal. The muscular work at the hip, knee and ankle joint was calculated using a model based upon dynamic mechanics described elsewhere. The mean peak concentric power output was, for the hip extensors, 74.4W, hip flexors, 18.0W, knee extensors, 110.1 W, knee flexors, 30.0 W and ankle plantar flexors, 59.4 W. At the ankle joint, energy absorption through eccentric plantar flexor action was observed, with a mean peak power of 11.4 W and negative work of 3.4 J for each limb and complete pedal revolution. The energy production relation- ships between the different major muscle groups were computed and the contributions to the total positive work were: hip extensors, 27%; hip flexors, 4%; knee extensors, 39%; knee flexors, 10%; and ankle plantar flexors 20%.

Key words: Bicycling -- Ergometer -- Power -- Work

Introduction

A considerable part of research in applied human physiology has been based on exercises on the bi-

Offprint requests to: M. O. Ericson, Department of Physical Medicine & Rehabilitation, Karolinska Institute, P. O. Box 60500, S 10401 Stockholm, Sweden

cycle ergometer, due to its easily standardized and measured resistance. The human power output and work generated during cycling has primarily been measured as, or calculated from, the energy transmitted to the ergometer braking system. This energy has most often been considered as equal to the work done by the leg muscles. Together with factors such as oxygen uptake, concentration of lactic acid and muscle fibre composition, calculated muscular work has been used in studies on physical fitness, energy expenditure, muscular work efficiency and different types of muscular metabolic functions.

To determine the power output from individual muscle groups, earlier authors have studied activities such as level walking and running. Elft- man (1940) and Cavagna et al. (1971 ; 1976) calculated the power output and work produced during level walking and running on the basis of changes in the body mass centre, However, Winter (1979) showed that there is an error in the assumption that the trajectory of the body centre of mass con- tains the information necessary for calculating the internal work done by the body. This error is par- ticularly important in symmetrical or reciprocal types of movement such as running or walking. Symmetrical but opposite movements of limb segments do not result in a centre of mass change, yet distinct kinetic energy changes have taken place. Today more mechanically accurate methods are available (Winter 1979; Gordon et al. 1980; Zar- rugh 1981; Williams and Cavanagh 1983). Gor- don et al. (1980) calculated the energy generation, absorption and transfer amongst segments during walking. They used two different terms for the mechanical power developed, "joint power" and "muscle power". The joint power was defined as the power delivered to or, if negative, taken from segments where they join due to the work done by

230 M.O. Ericson et al.: Power output and work in different muscle groups during ergometer cycling

the joint reaction forces. Muscular power was defined as the mechanical power delivered to or taken from segments where they join due to the work done by the muscle moments acting about the lower limb joints. The muscle power output in the different muscles surrounding these joints was calculated by multiplying the net moment of force by the angular velocity of joint movement.

Gordon et al. (1980) assumed that joint reaction moments acting on each segment were caused by muscle involvement alone. Contribu- tions to the joint reaction moments by such structures as the ligaments were assumed to be very small in moderate activity such as walking. The muscles surrounding a specific joint can generate mechanical energy and absorb energy by concentric and eccentric contraction respectively. Wil- liams and Cavanagh (1983) thoroughly discussed the problems of interpreting data on measured mechanical work during distance running, and all the sources of work and factors that will influence the relationship between mechanical work de- rived from cinematography and the metabolic work associated with it. In summary, positive work can have its origin from energy transfer, elastic energy and concentric muscular contra- tion: negative work can have its origin from non- muscular sources and eccentric muscular contra- tion.

Among the great number of studies that use bicycle ergometers, none concerns the instantaneous mechanical power output and work done at different joints performed by different muscle groups. The aim of the present study was to calculate the net power output and work generated at the hip, knee and ankle joints and to discuss the implications of muscular work for different muscle groups during ergometer cycling.

Materials and methods

Six subjects giving informed consent, all men aged between 20 and 31 years (mean 25.3 years), participated in the study. Their average height and weight were 1.80 m (SD= 0.06) and 71.3 kg (SD = 5.0) respectively. The subjects were students with ordi- nary recreational cycling experience. None of the subjects were suffering from hip, knee or ankle joint pain, or any other dysfunction of the locomotor system.

A bicycle ergometer (Cardionics with weight brakes, Car- dionics, Stockholm, Sweden) was used with a specially instru- mented left pedal in which a piezo-electric force transducer (Kistler type 9251 A) was mounted. With this equipment the forces in three orthogonal dimensions (x, y and z) could be measured (Ericson et al. 1984; 1985a). The forces were contin- uously recorded on a UV-recorder (Honeywell Visicorder 1508). A switch was mounted on the bicycle ergometer for

marking on the UV-record the top position of the crank (corresponding to zero and 360 degress crank angle) for each revolution. Time was recorded on the UV-recorder in parallel with the forces and the crank top position, using a specially de- signed time indication panel with a light emitting diode dis- play that gave a bar representation of time in units down to 1 millisecond. The test situations were filmed using a 16 mm cine-film camera (Paillard Bolex, 60 frames/second). The camera was mounted perpendicular to the sagittal plane of the subject at a distance of 3.5 m. As landmarks for the bilateral hip, knee and ankle joint-axes, dye marks were placed on the skin at a position approximately 1 cm anterior and superior to the tip of the greater trochanter, at the centre of the lateral epicondyle of the femur and at the tip of the lateral malleolus. The time was recorded on each film frame. A metronome ena- bled the subjects to find and maintain the chosen pedalling rate. When cycling, the trunk was inclined forward 20--30 ~ from the vertical. All subjects was allowed to warm up and familiarize themselves with the bicycle ergometer before the experiment.

The subjects cycled at a pedalling rate of 60 rpm and a workload of 120 W. The saddle height, defined as the greatest distance between the saddle and the upper surface of the pedal, was approximately 113% of the individual distance between the ischial tuberosity and the medial malleolus: it is also approximately 109% of symphysis pubis height, a distance which has been found to require the least oxygen consumption (Hamley and Thomas 1967; Nordeen-Snyder 1977). The foot position was defined as the position where the centre of the pedal was in contact with the head of the second metatarsal. The bicycle settings described above correspond to the "standardized ergometer cycling" mode defined and used in earlier work (Ericson et al. 1984; 1985a; 1985b; 1985c).

The subjects cycled for approximately 30 s before the measurements were taken. The subjects were filmed and the forces recorded for 5 seconds (approximately five revolutions). One revolution recorded on the UV-recorder was selected and analysed throughout the complete pedal cycle. The film was

\ ,

. . . .

. O f

I X ,~.

I

Fig. 1. Positions of the bilateral hip (H), knee (K) and ankle (A) joint axes, foot angle (q~z), pedal plane angle (~Y2), crank angle (q)) and pedal reaction forces Fz and Fx

M. O. Ericson et al.: Power output and work in different muscle groups during ergometer cycling 231

analysed with a projector (Analector ANL4), which made it possible to "freeze" the film and trace the picture at intervals of approximately 15 ~ crank angle. Hence, cine-film data was collected with a sampling rate of 60 Hz, while the kinematic data was later traced and analysed at a lower sampling rate of approximately 24 Hz. The positions for the hip (H), knee (K) and ankle (A) joint axes, the foot angle (~P2), pedal plane (cY2) and crank angle ((p) were then determined from the tracings (Fig. 1). The Fz and/~?c force values corresponding to each picture were read from the UV-recorder. Limb motion, moment of force and instantaneous power output were computed from crank angle, pedal plane angle, joint positions and pedal reaction forces.

The model for calcuations of hip, knee and ankle force moments and joint angular velocities used in the present study has been described in detail elsewhere (Bratt and Ericson 1985). To summarize; this model is based upon dynamic mechanics and takes into account the dynamically induced forces and moments due to forces of inertia and translational motions of the lower limb. In the model, the lower limb was treated as a 3-bar (foot, shank and thigh) linkage system of rigid bodies. The moment of inertia and centres of gravity were calculated using Dempster's anthropometrical data (1955). Angular velocities and accelerations were obtained by taking the first and second derivatives of the foot (q~2) and pedal plane 0y2) angles (Fig. 1) which were approximated by a sine wave. Similar simulations of the kinematics have been used earlier (Nordeen-Snyder and Cavanagh 1975; Hull and Jorge 1985). The model used in the present study (Bratt and Ericson 1985) is also generally similar to the model for biomechanical analysis of bicycle pedalling recently presented by Hull and Jorge (1985). The instantaneous mechanical power output (P) in the different muscle groups sorrounding each joint was estimated by:

P = M * w (1)

where

M = net moment of force (in Newton meters) w=joint angular velocity (in radians per second).

With the net muscular power output known, the work or energy (in Joules) produced during one pedal revolution about the joint was calculated.

Work= I Power dt (2)

Results

Load momen~.s duping cycling

20"

O-

-iO 90 180 270 360 Cr'ank angle { de 9 )

Fig. 2. Mean load moments acting about the bilateral hip, knee and ankle joint axes. Positive values indicate flexing hip, knee and dorsiflexing ankle load moment, counteracted by hip extensors, knee extensors and plantarflexors, respectively. 0 ~ and 360 ~ crank angles correspond to the top pedal position and 180 degrees to the bottom pedal position. O =Hip ; [] = Knee; A =Ankle

The calculated angular velocities (radians - s - 1) at the hip, knee and ankle joints during cycling at 60 rpm are shown in Fig, 4. A positive value of angular velocity indicates that the joint is extending. The knee joint angular velocity was approximately twice that of the hip and ankle joints.

The mean temporal hip, knee and ankle muscular power curves during the pedal revolution (zero to 360 degrees crank angle) are shown in Fig. 5. Positive power values indicates that power is produced in concentric contraction and negative values indicate negative work in eccentric contraction.

Muscular power at different hip, knee and ankle joint angles is shown in Fig. 6, and the respec- tive peak values are given in Table 1. There is a concentric hip extensor contraction (Fig. 6) from the most flexed hip joint position (point A) to the most extended position (C). Mean peak hip power (B) occurred at approximately 50 ~ hip angle. In the most extended position (C), where the

The mean load moments (counteracted by muscular action) acting about the hip, knee and ankle joints are shown in Fig. 2.

Figure 3 depicts the mean joint motions during ergometer cycling. The ankle joint motion described in Fig. 3 does not correspond to the clini- cally used foot angle, defined by AAOS (1965). The present ankle joint angle is defined as the anterior angle between the shank and a line between the medial malleolus and the head of the second metatarsal, i.e. at the centre of the pedal surface (Fig. 1).

Join( too{ions duping cycling 180]

150

~ 6o

;q 3o

0 90 180 270 360 Crank ang le { dog l

Fig. 3. Mean hip, knee and ankle joint angles (y-axis) at various crank angles (x-axis). O =Hip ; [] =Knee ; A =Ankle


5" ~ q.

-~ o~

-2- -3-

-s

Join{_ angu ta r ve toc i ty

90 180 270 Crank an 9{e [deg !

360

Fig. 4. Calculated mean hip, knee and ankle joint angular velocities at various crank angles (x-axis). �9 = Hip; [] = Knee; /x = Ankle

I'lusculav power during cycling 125"

75-

~ 50-

~ 25- [

-2'. - - s b ~-i7o ~o 3~o Crank angte (de 9)

Fig. 5. Hip, knee and ankle muscular power output (y-axis) at various crank angles (x-axis). �9 =Hip ; [] =Knee ; A =An- kle

hip joint rotation changed from extension to flexion, there was a low peak of negative hip power. During hip flexion, the power produced (D) by the hip flexor muscles was mainly concentric.

During knee extension (Fig. 6) positive power was produced by the knee extensors, with a peak (F) at 80 ~ knee angle. When knee flexion oc-

~. 125"

i00.

75 ~

50-

~ 25-

~: 0 - - -

Hip power

B

25 50 75 Hip angle (de 9)

.~, 125-

iO0

75 o~ m. 50

2s

z: 0

-25 - / /

Knee power F

50 7S I00 Knee angle Cde 9)

125

I00

7s

25

Flnk/e power

--/h--

J

K & I - - L

7'5 1 O0 125 R'nk [e angle, (de9 1

Fig. 6. Hip, knee and ankle muscular power output (y-axis) related to the hip, knee and ankle joint angles (x-axis), respectively

curred (G to E) positive power was produced by the knee flexor muscles.

There was a dorsiflexing ankle load moment throughout the complete revolution (Fig. 2). Hence, only the plantar flexors produced or absorbed energy. During ankle joint extension (plantar flexion) (Fig. 6) between points 1 to J to K, positive power was present. During approximately 50% of the motion cycle (K to L to I) energy was absorbed through plantar flexor action.

66.8 J was produced by the leg muscles in positive work and 6.0 J was absorbed in negative work. Mean peak power values, muscular work and the energy production relationship between the different major muscle groups are shown in Table 1. At the ankle joint, energy absorption, most probably deriving from eccentric plantar flexor action, was present with a mean peak power of 11.4 W and negative work of 3.4 Joule (J) for each limb and complete pedal revolution.

Discussion

In the present study only one pedal was equipped with a force transducer. Symmetry between leg actions has been assumed when discussing the total amount of work and power output. Asymmetry between the lower limbs during ergometer cycling has been reported (Daly and Cavanagh 1976; Sar- geant and Davies 1977; McCartney et aL 1983). However, contrary to these findings, Sargeant et al. (1981) did not find any consistent pattern of asymmetry between the legs during cycling. Thus, it cannot be ruled out that the possible presence of asymmetry may have influenced the results.

As the crank velocity could not be properly determined from the cine-film recordings due to the low frequency of frame analysis (approximately 24 Hz), the pedalling rate was considered


Table 1. Mean muscular energy (J) produced (concentric work) and absorbed (eccentric work) and peak power output (W) during ergometer cycling at 120 W, 60 rpm, mid-saddle height and anterior foot position. (n = 6)

Concentric work Eccentric work

Peak power Energy % of Peak power Energy % of (W) (J) total (W) (J) total mean (SD) mean (SD) concentric mean (SD) mean (SD) eccentric

work work

Hip extensors 74.4 (29.4) 18.1 (6.1 27 8.9 (6,7) 2.0 (1.7) 32 flexors 18.0 (6.6) 2.4 (1.2) 4 0.0 (0.0) 0.0 (0.0) 0

Knee extensors 110.1 (25.9) 25.9 (6.7) 39 4.5 (2.1) 0.4 (0.4) 7 flexors 30.0 (10.5) 6.6 (2.4) 10 8.3 (8.6) 0.2 (0.4) 4

Ankle plantar flexors 59.4 (12.1) 13.8 (3.6) 20 11.4 (4.1) 3.4 (1.3) 57

to be constant throughout the complete pedal revolution. Recent studies (Bratt and Ericson 1985; Hull and Jorge 1985) have shown that this is a fair assumption. In addition, constant angular velocity of the cranks has been assumed in earlier studies on work output during cycling (Cavanagh et al. 1974; Daly and Cavanagh 1976).

The lower limb does not rotate significantly about any vertical axis, and the rotational joint motions about the anterio-posterior axes are small and slow (Ericson et al. 1984). Therefore, the present calculation model deals only with the forces and moments acting in the sagittal plane, while those acting in the frontal and horizontal planes and the muscular work related to limb movements in these planes have been disre- garded.

The moments of force calculated in our study are the net moments, i.e. the presence of co-contraction in the muscles surrounding the hip, knee and ankle joints has not been taken into account. This limitation applies to most biomechanical models concerning moments and forces acting about the lower limb joints during activities such as level walking or stair-climbing (Morrison 1968; Andriacchi et al. 1980; Boccardi et al. 1981). However, in a recent study quantifying the magnitude of lower limb muscular activity during ergometer cycling (Ericson et al. 1985b), co-contra- tion was found between the flexor and e,xtensor muscles surrounding the knee joint, but since counteracting moments caused by co-contracting muscles are unpredictable, it is hard properly to determine the true instantaneous muscular power output. Therefore, the muscular power output values reported here must be viewed as minimum values, and the influence of co-contracting muscles on the total muscular power output during cycling needs further investigation.

The muscular power output and work obtained during cycling can be compared with the muscular power output and work during level walking (Gordon et al. 1980) and slow jogging (Winter 1983), in which the hip and knee muscles work both concentrically and eccentrically. The knee extensor muscles absorb 3.6 times as much energy as they generate during slow jogging (Winter 1983). The great amount of eccentric muscular work during walking and jogging is in con- trast to that in cycling, where the hip, knee and ankle joint muscles mainly work concentrically. During "standardized" ergometer cycling (i.e. with the bicycle ergometer set as in the present study) the ankle plantar flexor muscles generate 4.1 times as much energy as they absorb, compared with 2.9 times during jogging. Thus, one may conclude that during cycling the lower limb muscles generate energy mainly by concentric contractions, compared to level walking and jogging where they work both concentrically and eccentrically in approximately equal proportions. However, it is important to note that cycling is not a purely concentric work exercise, which as far as we known, has been the assumption hi- therto (Abbot et al. 1952; Bigland-Ritchie et al. 1973; Zacks 1973; Knuttgen et al. 1982; Piemen- tal et al. 1982). Our results indicate that both eccentric and concentric work was performed mainly by the plantar flexors, and this must be considered when estimating the energy cost and efficiency of concentric and eccentric muscular work.

As earlier discussed by, for example, Williams and Cavanagh (1983), work can be transferred through the action of two-joint muscles. As an example, some of the negative work absorbed at the ankle joint (3.4 J) might have been transferred to the knee joint by the gastrocnemius muscle, which


can act both as a knee flexor and an ankle plantar flexor. Since gastrocnemius medialis does not significantly change its muscular activity (Ericson et al. 1985b) when the ankle load moment as approximately doubled when changing foot position from a posterior position to the anterior one used in the present study (Ericson et al. 1985), it is most likely to have been the soleus muscle that increased its activity to produce or absorb the majority of the work at the ankle. The soleus muscle also has a higher peak activity (37% of the maximum time averaged EMG) than the 19 and 32% for the medial - lateral heads of gastrocnemius. In addition, the medial head of gastrocnemius significantly increased its activity when the pedalling rate was increased (Ericson et al. 1985b). Such speed increase significantly enhanced the extending knee load moment (Ericson et al. 1985c) while it did not simultaneously change the ankle load moment. Therefore, it seems reasonable to assume that during cycling the gastrocnemius medialis muscle acts more as a knee joint flexor than an ankle plantar flexor. The possible coupling effect by the gastrocnemius and other two-joint muscles such as biceps femoris and the medial hamstring might influence muscular power output, and this needs further investigation.

The majority of negative work at the ankle is most probably absorbed by soleus in eccentric work (3.4 J), while the small amounts of eccentric hip and knee power reported must be treated and interpreted more carefully. Negative hip and ankle power were present when the lower limb was more or less passively flexed during the passive power phase (195 to 360 degrees crank angle). During this period, energy was supplied through the pedals to the flexing limb from the contrala- teral leg extension movement, i.e. the active limb supplied the passive limb with some of the energy necessary to lift it between approximately 195 ~ and 360 ~ crank angle (passive phase). Ericson et al. (1985b) quantified the magnitude of EMG activity during cycling and found that hip extensor activity during "standardized" ergometer cycling never exceeded 12% of the maximum time averaged EMG. During the passive phase there is hardly any hip extensor activity. Hence, the negative hip extensor power is probably mainly passively transmitted through the hip joint, and conse- quently no eccentric work is done by the hip extensors. The eccentric work found at the knee joint was very small (0.4 J and 0.2 J) which might be explained by an error of calculation.

The biomechanical method used in the present study makes it possible to calculate net muscular

work, including both "external" work (work supplied to the braking system) and "internal" work (limb motion work). As recently pointed out by Williams (1985), the internal work during cycling has not yet been properly determined. Hence, the human mechanical efficiency for cycling has hith- erto been underestimated (Williams 1985). The method for calculation of joint and muscular power during level walking reported by Gordon et al. (1980), used in the present study for the analysis of cycling, will be useful for further ana- lyses of human mechanical efficiency.

As described above, several assumptions have been made to allow the calculations of muscular power output and work done during ergometer cycling. Nevertheless, the method used in the present study provides an estimation of the work produced or absorbed by different muscle groups. The work done by different muscle groups, such as the 25 �9 9 J produced by quadriceps femoris in concentric contraction, may be compared with data on EMG activity, levels of lactic acid, muscle fibre composition and oxygen consumption. In- vestigations on the mechanical work done by cer- tain major muscle groups during cycling may therefore provide data useful in research on muscular metabolism, such as energy expenditure and the production of various metabolites measured per unit muscle weight.

Acknowledgements. This study was supported by grants from the Swedish Medical Research Council (5720) and the Karo- linska Institute.

References

Abbot BC, Bigland B, Ritchie JM (1952) The physiological cost of negative work. J Physiol (Lond) 117:380--390

Andriacchi TP, Andersson GBJ, Ferlier RW, Stern D, Galante JO (1980) A study of lower-limb mechanics during stair- climbing. J Bone Joint Surg 62-A:749--757

American Academy of Orthopaedic Surgeons (1965) Joint motion: method of measuring and recording. 4th reprint 1969. E. & S. Livingstone Ltd., Edinburgh

Bigland-Ritchie B, Graichen H, Woods JJ (1973) A variable- speed motorized bicycle ergometer for positive and negative work exercise. J Appl Physiol 35:739--740

Boccardi S, Pedotti A, Rodano R, Santambrogio GC (1981) Evaluation of muscular moments at the lower limb joints by an on-line processing of kinematic data and ground reaction. J Biomech 14:35--45

Bratt A, Ericson MO (1985) Biomechanical model for calculation of joint loads during ergometer cycling. TRITA-MEK 85-06, ISSN 0348-467X

Cavagna GA, Komarek L, Mazzoleni S (1971) The mechanics of sprint running. J Physiol 217:709--721

Cavagna GA, Thys H, Zamboni A (1976) The sources of external work in level walking and running. J Physio1262: 639--657


Cavanagh PR, Petak KL, Shapiro R, Daly D (1974) Bilateral asymmetry in work output during cycle ergometer exercise. Med Sci Sports 6:80--81

Daly D J, Cavanagh PR (1976) Asymmetry in bicycle ergometer pedalling. Med Sci Sports 8:204--208

Dempster WT (1955) Space requirements of the seated opera- tor, WADC Technical report, (Wright Patterson Air Force Base Development Center): 55-- 159

Elftman H (1940) The work done by muscles in running. Am J Physiol 129:672--684

Ericson MO, Nisell R, Ekholm J (1984) Varus and valgus loads on the knee joint during ergometer cycling. Scand J Sports Sci 6:39--45

Ericson MO, Ekholm J, Svensson O, Nisell R (1985a) The forces on ankle joint structures during ergometer cycling. Foot & Ankle 6:35--142

Ericson MO, Nisell R, Arborelius UP, Ekholm J (1985b) Mus- cular activity during ergometer cycling. Scand J Rehab Med 17:53--61

Ericson MO, Bratt ,~., Nisell R, N6meth G, Ekholm J (1986c) Load moments about the hip and knee joints during ergometer cycling. Scand J Rehab Med (in press)

Gordon D, Robertson E, Winter DA (1980) Mechanical energy generation, absorption and transfer amongst segments during walking. J Biomech 13:845--854

Hamley EJ, Thomas V (1967) Physiological and postural factors in the calibration of the bicycle ergometer. J Physiol 191:55--57

Hull ML, Jorge M (1985) A method for biomechanical analysis of bicycle pedalling. J Biomech 18: 631--644

Knuttgen HG, Patton JF, Vogel JA (1982) An ergometer for concentric and eccentric muscular exercise. J Appl Physiol 53:784--788

McCartney N, Heigenhauser GJF, Sargeant AJ, Jones NL (1983) A constant-velocity cycle ergometer for the study of dynamic muscle function. J Appl Physiol 55:212--217

Morrison JB (1968) Bioengineering analysis of force actions transmitted by the knee joint. Bio Med Engin 3:164--170

Nordeen-Snyder KS (1977) The effect of bicycle seat height variation upon oxygen consumption and lower limb kinematics. Med Sci Sports 2:113-- 117

Piemental NA, Shapiro Y, Pandolf KB (1982) Comparison of uphill and downhill walking and concentric and eccentric cycling. Ergonomics 25:373 --380

Sargeant AJ, Davies CTM (1977) Forces applied to cranks of a bicycle ergometer during one- and two-leg cycling. J Appl Physiol 42:514--518

Sargeant A J, Hoinville E, Young A (1981) Maximum leg force and power output during short-term dynamic exercise. J Appl Physiol 51:1175--1182

Williams KR (1985) The relationship between mechanical and physiological energy estimates. Med Sci Sports 17:317--325

Williams KR, Cavanagh PR (1983) A model for the calculation of mechanical power during distance running. J Bio- mech 16:115--128

Winter DA (1979) A new definition of mechanical work done in human movement. J Appl Physiol 46:79--83

Winter DA (1983) Moments of force and mechanical power output in jogging. J Biomech 16:91--97

Zacks RM (1973) The mechanical efficiencies of running and bicycling against a horizontal impeding force. Int Z Angew Physiol 31:249--258

Zarrugh MY (1981) Power requirements and mechanical efficiency of treadmill walking. J Biomech 14:157--165

Accepted February 19, 1986