Upsala J Med Sci 87: 223-233, 1982 Evaluation of a Dynamometer for Measurement of Isometric and Isokinetic Torques Martin Ericsson' , Kurt Johansson', Bengt Nordgren' , Lars-Olof Nordesjo' and Octavia Borges' From the Department of Medical Rehabilitation', University Hospital, Uppsala, the Institute of Physics', Uppsala University, Uppsala and the Department of Clinical Physiology3, Gavle Hospital, Giiule, Sweden ABSTRACT A modified version of the original Cybex I1 dynamometer with a temperature compensated strain gauge transducer has been evaluated. It was found that the calibration constant was dependent of the vertical load of the device. The ra- tio (k) between the applied and the recorded torque is angle independent du- ring extension and k is equal to 1.18 and during flexion k is angle dependent and can be expressed as k= -.0008 0 + 1.208, where 0 is the angle of flexion. COMMENTS ON TEE MODEL It is important for clinicians involved in rehabilitating physically dis- abled patients to be able to measure changes in muscular performance and strength. The muscles are working both isometrically and dynamically. During the early 1960's, J J Perrine developed the concept of isokinetic exercise, i.e. dynamic movement with a constant speed, and it was first reported by His- lop and Perrine in 1967 (1). The Cybex I1 dynamometer* has during some years been used clinically for measurement of isometric and isokinetic torques ( 2 , 3 , 4, 5 ) . A modified ver- sion of the original device has recently been described (6). In the original device the torque was sensed via an oilcell. However, the output signal of the transducer was not linear, a factor which made a simple correction of the re- corded data difficult. Therefore a new device has been developed which senses the torque by means of a strain gauge technique.** The aim of this study has been to investigate the calibration conditions of the modified device in order to be able to present valid data. Dynamometer In this modified version of the original Cybex I1 dynamometer the hydraulic pressure gauge was replaced by a temperature compensated strain gauge transdu- * Cybex Division of Lumex, 100 Spence Street, Bay Shore, N.Y. 11706 ** Aeronautical Research Institute of Sweden 223 cer ( 6 ) . A b l o c k diagram of t h e measuring system i s p r e s e n t e d i n F i g u r e 1. S t r a i n gauge Amp1 i f 1 er Y transducer Tektronix ’ Goniorneter Amp1 i f i e r X Cybex I1 . X Y Recorder Bryan 26700 High Speed F i g . 1. Block diagram of t h e measuring system. I n t h e y - a m p l i f i e r l i n e t h e r e i s a c a l i b r a t i o n s i g n a l , which c o r r e s p o n d s t o a t o r q u e e q u a l t o 50 Nm. Using t h i s s i g n a l as c a l i b r a t i o n t h e r e s u l t i s deno- t e d t h e r e c o r d e d t o r q u e . I n t h e p r e s e n t s t u d y t h e s i g n a l from t h e s t r a i n gauge t r a n s d u c e r h a s been c a l i b r a t e d . C o r r e c t i o n f o r t h e g r a v i t a t i o n a l t o r q u e due t o t h e mass of t h e l e v e r arm and t h e l i m b The mechanical arrangement f o r measurement of t h e t o r q u e (M) i s i l l u s t r a t e d i n F i g u r e 2 . knee \--k joint 224 Fig. 2 . Mechanical arrangement f o r measurement of t h e t o r q u e (M) d u r i n g knee e x t e n s i o n and f l e x i o n a t a c o n s t a n t angular v e l o c i t y . F = t h e f o r c e produced by t h e limb. l1 = d i s t a n c e between t h e c e n t e r of mass of t h e limb and l e v e r arm and t h e a x i s of t h e knee j o i n t . l2 = d i s t a n c e between t h e p o i n t where t h e l e v e r a r m is a t t a c h e d t o t h e l i m b and t o t h e a x i s of t h e knee j o i n t . 8 = t h e f l e x i o n angle; 8 = Oo when t h e l e g i s f u l l y extended. mg = t h e weight of t h e l e v e r arm and t h e limb. Due t o t h e f o r c e of g r a v i t a t i o n on t h e l e v e r arm and t h e limb a c o r r e c t i o n must be made f o r t h e g r a v i t a t i o n a l t o r q u e (M ) ( 7 ) . Using t h e d e f i n i t i o n s i n Figure 2 t h e formula f o r t h i s c o r r e c t i o n i s d e r i v e d a s follows: M = F 1 2 ( a ) M = m g l1 cos 8 ( b ) M = M + M e x t e n s i o n of t h e knee j o i n t ( C ) M = M - M f l e x i o n of t h e knee j o i n t ( d ) 9 4 r e g 9 r e g g The c o n s t a n t g i s t h e g r a v i t a t i o n a l a c c e l e r a t i o n and i s equal t o 9.81 m / s and M M t h e l i m b r e l a x e d . The r e s u l t of t h i s measurement i s c a l l e d M' is t h e recorded t o r q u e . The g r a v i t a t i o n a l t o r q u e 0 r e g i s measured a t an angle Go, i . e . Go = 0 w i t h t h e muscles of g g ' The e q u a t i o n M = M ' cos 0 g g a ( e ) i s t h e n used when c a l c u l a t i n g t h e t o r q u e of t h e l e v e r a r m and t h e limb a s a f u n c t i o n of t h e angle 8 i n t h e e q u a t i o n s (c) and ( d ) above. C h a r a c t e r i s t i c s of t h e recorded t o r q u e The recorded t o r q u e of t h e knee j o i n t f o r both e x t e n s i o n and f l e x i o n i s shown i n F i g u r e s 3 and 4 i n which t h e angular v e l o c i t y i s equal t o 1 2 and 150 d e g r e e s / s , r e s p e c t i v e l y . The t o r q u e of t h e g r a v i t a t i o n a l f o r c e of t h e limb F i g . Fig. 1 a = a 2 = a3 = a4 = Fig. C and l e v e r a r m i s a l s o p r e s e n t e d i n both f i g u r e s and i s denoted (a3 i n 3 and a i n Fig. 4 ) . 3 . Recorded torque (M t o r q u e of a 5 kg weight hanging a t t h e o u t e r end of t h e l e v e r a r m . e x t e n s i o n of t h e knee j o i n t . g r a v i t a t i o n a l torque of t h e l i m b and t h e l e v e r a r m a t 1 2 O / s . f l e x i o n of t h e knee j o i n t . 4. Recorded t o r q u e of a s u b j e c t a t 15Oo/s a n g u l a r v e l o c i t y . 5 ) of a s u b j e c t a t 1 2 O / s angular v e l o c i t y . r e g 0 aJ and a6 i s t h e g r a v i t a t i o n a l t o r q u e of t h e limb and t h e l e v e r a r m a t 1 2 / s and 150 / s r e s p e c t i v e l y . M = peak overshoot. 0 P 225 Fig. 3 . Fig. 4. 226 The r e c o r d e d t o r q u e o f a 5 kg weight hanging a t t h e o u t e r end o f t h e l e v e r a r m i s c a l l e d a' i n F i g u r e 3 . From t h a t p a r t of t h e f i g u r e it i s concluded t h a t t h e r e i s a damped frequency of t h e c o n t r o l system e q u a l t o 10 2 Hz. T h i s f r e q u e n c y of t h e c o n t r o l system i s a l s o found i F i g u r e 4 . T h i s o s c i l l a - t i o n i s damped o u t a f t e r 4-5 p e r i o d s . The same damped o s c i l l a t i o n s c a l l e d a L i n F i g u r e 3 a r e a l s o seen i n t h e r e c o r d e d t o r q u e o f t h e knee j o i n t b o t h i n ex- t e n s i o n and i n f l e x i o n movement. When comparing t h e r e c o r d i n g s a' and a3 it i s obvious t h a t it i s d i f f i c u l t t o keep t h e muscles r e l a x e d d u r i n g t h e whole movement. The c o r r e c t i o n t e r m s of t h e e q u a t i o n s c and d s h o u l d t h e r e f o r e be measured w i t h t h e limb r e s t i n g a t a f i x e d a n g l e ( O O ) . The g r a v i t a t i o n a l t o r - que M i s t h e n c a l c u l a t e d u s i n g t h e e q u a t i o n e . 9 The r e c o r d e d t o r q u e o f t h e g r a v i t a t i o n a l f o r c e o f t h e l e v e r a r m and t h e limb a r e a l s o shown i n F i g u r e 4 . The a n g u l a r speed i s 1 2 / s i n t h e r e c o r d i n g a 5 and 15Oo/s i n a . The peak o v e r s h o o t (M ) o f t h e 10 H z o s c i l l a t i o n i n c r e a - s e s when t h e a n g u l a r v e l o c i t y i s i n c r e a s e d . The v a l u e o f t h e second peak i n - c r e a s e s from 6 Nm a t 1 2 / s t o 1 2 Nm a t 150 / s . These l a r g e peaks o r i g i n a t i n g from t h e a n g u l a r v e l o c i t y c o n t r o l system of t h e Cybex I1 makes it d i f f i c u l t t o c a l c u l a t e a v a l i d maximum v a l u e of t h e r e c o r d e d t o r q u e , which a l s o h a s been p o i n t e d o u t by Winter e t a1 ( 7 ) . T h i s d i f f i c u l t y i s d e m o n s t r a t e d i n F i g u r e 5 , which i s a c a l c u l a t e d u n i t - s t e p r e s p o n s e of a t h i r d o r d e r c o n t r o l system. The a p p l i e d t o r q u e M used i n t h e c a l c u l a t i o n c o r r e s p o n d s t o t h e maximum t o r q u e , and t h e f i g u r e shows t h a t t h e r e c o r d e d t o r q u e of t h e system h a s a peak o v e r - s h o o t (M ) . Concequently t h e mean v a l u e c u r v e can be used g i v i n g t h e a p p l i e d t o r q u e . 0 6 P 0 0 P t i m e F i g - 5. A c a l c u l a t e d u n i t - s t e p r e s p o n s e of a t h i r d o r d e r system. M = a p p l i e d t o r q u e ; M = r e c o r d e d t o r q u e ; M = peak o v e r s h o o t . P 227 1 T h i s is a l s o e x a m p l i f i e d i n Figure 3 i n t h e r e c o r d i n g ( a ) as a dashed l i n e . There i s a l s o i n F i g u r e 3 an o s c i l l a t i o n w i t h a lower frequency which i s e q u a l t o 1 . 6 2 0 . 2 Hz. T h i s frequency i s probably n o t due t o t h e c o n t r o l sys- t e m b u t t o t h e mechanical arrangement of t h e l e v e r arm. The peaks of t h i s f r e - quency a r e marked w i t h a* where t h e y a r e most e v i d e n t , b u t t h e y can a l s o be seen a t some of t h e a -peaks. The same o s c i l l a t i o n i s a l s o seen i F i g u r e s 7 and 8 where a c o n s t a n t t o r q u e i s a p p l i e d t o t h e l e v e r a r m . I t i s t h e r e f o r e con- cluded t h a t t h i s frequency i s n o t g e n e r a t e d by t h e muscles. C a l i b r a t i o n 1. Extension of t h e knee j o i n t 2 The t o t a l f o r c e a c t i n g on t h e s t r a i n gauges d u r i n g t h e e x t e n s i o n and f l e x - i o n movement of t h e knee j o i n t may i n f l u e n c e t h e r e s u l t of t h e measurement. I n t h i s p r e s e n t a t i o n t h e e x t e n s i o n movement t h i s f o r c e i s d i r e c t e d upwards and v a r i e s from 0 N t o 350 N and i n t h e f l e x i o n movement between 0 N t o 300 N. A s p e c i a l c a l i b r a t i o n equipment w a s t h e r e f o r e c o n s t r u c t e d i n o r d e r t o o b t a i n a s i m i l a r v e r t i c a l l o a d as d u r i n g an a c t u a l i n v e s t i g a t i o n of a s u b j e c t . The ex- p e r i m e n t a l equipment f o r t h e c a l i b r a t i o n i s shown s c h e m a t i c a l l y i n F i g u r e s 6a and 6b. Two d i s c s o f aluminium w i t h t h e r a d i u s e q u a l t o 0.15 m and 0.49 m r e s - p e c t i v e l y w e r e used. P C y b e x I t n l e v e r D i_s_c p i g . 6a 228 F i g . 6b F i g . 6. C a l i b r a t i o n s e t - u p . The weight used t o produce a c o n s t a n t t o r q u e i s connected t o t h e l e v e r arm v i a a w i r e and a d i s c . The t o t a l f o r c e a c t i n g on t h e l e v e r arm i s e q u a l t o t h e d i f f e r e n c e between t h e weight of t h e d i s c and m a s s ( m ) i n Figure 6a and t o t h e sum of t h e masses i n Figure 6b. I n t h e experiment shown i n Figure 6a t h e v e r t i c a l f o r c e a c t i n g on t h e a x i s of r o t a t i o n i s equal t o t h e sum of t h e weight of t h e d i s c ( 2 5 kg o r 3 kg) and t h e hanging weight ( m ) . I n Figure 6b t h e v e r t i c a l f o r c e i s e q u a l t o t h e d i f - f e r e n c e between t h e weights of t h e two masses. The r e s u l t s of t h i s experiment a r e p r e s e n t e d i n F i g u r e s 7 and 8 which corresponds t o F i g u r e s 6b and 6a res- pec t i v e l y N I736 m = 3 0 k g 1 ~ 0 - w 0' 1 8 0 ' 3 6 0' m = 2 0 k g 1 8 0 ' 3 60' 1 4 4 2 2 0' m = l O k g 1 3 4 3 3 0' 180' 3d 0' r = 0 . 4 9 m Fig. 7 . Recorded t o r q u e f o r d i f f e r e n t weights ( m ) . The c a l i b r a t i o n configura- t i o n i s also shown. The t o t a l v e r t i c a l f o r c e a c t i n g on t h e equipment i s given t o t h e l e f t of t h e f i g u r e . Angular v e l o c i t y = 12O/s. 229 N m = 5 0 k g I 2 4 5 m = 3 0 k g - m = 2 0 k g 149- m = 1 0 k g I 1 4 7 , 8 9 0 6 0 3 0 0 F i g . 8. Recorded t o r q u e f o r d i f f e r e n t w e i g h t s ( m ) . The c a l i b r a t i o n c o n f i g u r a - t i o n i s also shown. Angular v e l o c i t y = 1 2 / s . 0 The r e c o r d e d t o r q u e i n F i g u r e I shows an a n g u l a r dependence and t h e c a l i - b r a t i o n must t h e r e f o r e be made under s i m i l a r c o n d i t i o n s as d u r i n g a c l i n i c a l i n v e s t i g a t i o n . The c u r v e s i n b o t h f i g u r e s f o r m = 50 kg i n d i c a t e t h a t a s t h e r e i s no a n g u l a r dependence o f t h e c a l i b r a t i o n c o n s t a n t i n F i g u r e 8, t h e c a l i b r a - t i o n s e t - u p i n F i g u r e 6 a c o r r e s p o n d s q u i t e w e l l t o t h e c l i n i c a l s i t u a t i o n i n t h e e x t e n s i o n movement of t h e knee j o i n t . The r e s u l t s from F i g u r e 8 a r e g i - ven i n Table I and t h e d a t a c o r r e s p o n d i n g w i t h i n e r r o r s t o a s t r a i g h t l i n e . I t i s concluded from T a b l e I t h a t t h e r e c o r d e d t o r q u e of t h e e x t e n s i o n movement h a s t o be m u l t i p l i e d by t h e c a l i b r a t i o n f a c t o r 1.18 i n o r d e r t o g i v e t h e ac- t u a l t o r q u e of a s u b j e c t . 230 Angle 90 70 50 30 1 0 Applied t o r q u e ( N m ) 48 96 144 240 Recorded t o r q u e (Nm) 41 82 38 80 36 79 35 78 34 78 23 21 3 23 21 3 23 21 3 23 21 3 23 21 3 Table I . Recorded t o r q u e from t h e c a l i b r a t i o n a c c o r d i n g t o t h e s e t - u p i n F i g . 6a ( e x t e n s i o n ) . The radium o f t h e d i s c e q u a l s 0.49 m . 2 . F l e x i o n of t h e knee j o i n t The c a l i b r a t i o n s e t - u p f o r t h e f l e x i o n movement i s i l l u s t r a t e d i n F i g u r e 9 . F i g . 9. C a l i b r a t i o n s e t - u p c o r r e s p o n d i n g t o t h e f l e x i o n movement of t h e knee j o i n t . The r a d i u s o f t h e d i s c i s 0.15 m . T h i s w a s used t o produce a v e r t i c a l downward f o r c e c o r r e s p o n d i n g t o f l e x - i o n o f t h e knee j o i n t . The downward v e r t i c a l f o r c e i s t h e sum of ml and t h e weight o f t h e wheel ( 3 kg) minus t h e upward v e r t i c a l f o r c e g e n e r a t e d by m 2 ’ The r e c o r d e d t o r q u e s f o r d i f f e r e n t v e r t i c a l l o a d s o f t h e r o t a t i o n a x i s are 23 1 shown i n Figure 10. 1 . e I 0 I 9 0 5 0 r = 0 . 1 5 m F i g . 10. Recorded t o r q u e f o r d i f f e r e n t weights ml and m2. The c a l i b r a t i o n con- f i g u r a t i o n i s a l s o shown. The t o t a l v e r t i c a l f o r c e a c t i n g on t h e equipment i s given t o t h e l e f t of t h e f i g u r e . Angular v e l o c i t y = 1 2 / s . 0 The conclusion from Figure 10 i n t h i s case i s t h a t t h e c a l i b r a t i o n con- s t a n t i s angular dependent. The r e s u l t of t h e c a l c u l a t i o n of t h e c o n s t a n t where t h e d a t a i n Figure 10 was used i s shown i n Figure 11. k T 1 l * l O L .oo 0 3 0 6 0 9 0 8 232 Fig. 11. C a l i b r a t i o n c o n s t a n t ( k ) f o r f l e x i o n a s a f u n c t i o n o f t h e angle 8. k = a p p l i e d t o r q u e divided by recorded torque. The v e r t i c a l a x i s k i s equal t o t h e a p p l i e d t o r q u e divided by t h e recorded one. The c a l i b r a t i o n c o n s t a n t i s expressed i n numerical v a l u e s a s k = -0.0008 8 + 1.208, where t h e angle of f l e x i o n of t h e knee j o i n t defined i n Figure 2 . CONCLUSION I t was found i n t h i s study t h a t t h e c a l i b r a t i o n c o n s t a n t ( k ) f o r t h e dyna- mometer used i n our l a b o r a t o r y d i f f e r s between e x t e n s i o n and f l e x i o n movement of t h e knee j o i n t . The c o n s t a n t i s defined a s t h e r a t i o between t h e a p p l i e d and recorded t o r q u e . During e x t e n s i o n k i s angle independent and e q u a l s 1.18, -.0008 9 + 1.208, where 8 is t h e angle of f l e x i o n of t h e knee j o i n t . ACKNOWLEDGEMENT This work was supported by t h e Swedish Medical Research Council Grant No. 1156 ( M . E . ) 1. 2. 3 . 4 . 5. 6. 7 . REFERENCES Hislop, H . J . and P e r r i n e , J.J.: The i s o k i n e t i c concept of e x e r c i s e . J Am Phys Ther Assoc 47:114-117, 1967. Murray, P., Gardner, G.M., Mollinger, L.A. and Sepic, S.B.: S t r e n g t h of i s o m e t r i c and i s o k i n e t i c c o n t r a c t i o n s . Knee muscles o f men aged 20-86. Phys Ther 60-412, 1980. 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Address f o r r e p r i n t s : Martin E r i c s s o n , M.D. Dept of Rehab Med U n i v e r s i t y Hospital 5-750 1 4 Uppsala Sweden 233