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Morphological Analysis of Force/Velocity Relationship in Dynamic Exercise at Varying Loads

Limonta, Eloisa1; Sacchi, Massimiliano2

Journal of Strength and Conditioning Research: August 2010 - Volume 24 - Issue 8 - p 2065-2072
doi: 10.1519/JSC.0b013e3181db23ac
Original Research

Limonta, E and Sacchi, M. Morphological analysis of force/velocity relationship in dynamic exercise at varying loads. J Strength Cond Res 24(8): 2065-2072, 2010-This study examined the force/velocity (F/V) curve morphology among the entire concentric phase of the countermovement squat (CMS). The hypothesis is that F/V curve shape of the lower limb muscles complex is different from F/V isolated muscle curve and that these analyses could be useful in characterizing athletes' muscular capacity and training programs. Squat exercise was performed by 29 subjects (15 men and 14 women, divided into resistance and endurance athletes). The protocol was 6 × 1 CMS at maximal speed with increasing loads: 20, 35, 50, 65, 80, 90% of 1 repetition maximum (1RM). Displacement, speed, and acceleration of the weight bar, joint knee angles, knee angular speed, and total and normalized forces were collected. F/V relation was obtained by force and velocity values of each 10° angular interval of the concentric phase for any load. Results show that the F/V relationship does not follow a linear shape and an equivalent criterion for all loads. We observed a “second peak force” statistically higher (p < 0.05) than the inversion peak at 80 and 90% 1RM. Resistance trained men showed a “second peak” higher and larger than that shown by endurance trained men. This indicated a higher ability to produce and maintain greater force at higher relative speed. These results may be helpful to identify the muscle characteristics of the athletes at various speeds and joint positions. With a phase division of the specific move, it will be possible to determine an individualized program to monitor the specific phases of technical moves and to evaluate the training effect in long run.

1Department of Sport Sciences, Nutrition and Health, Statal University of Milan, Milan, Italy; and 2Research and Development Department, Vibram Spa, Albizzate, Italy

Address correspondence to Limonta Eloisa,

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Lower limb force evaluation is a fundamental study in sport-related studies, both for training programs and as performance indices. The Squat is the most used and appropriate exercise for this type of evaluation because of the great number of joints and large muscles involved, and for its similarity to many athletetic movements. The Squat is a versatile exercise and can be executed in different ways; this means that it is a specific evaluation instrument with laboratory results well related to field activities.

Force/velocity relation (F/V) is a muscle performance index; this relation has already been examined in monojoint isokinetic (15) and ballistic (17) movements other than in cyclic multijoint movements (10).

Isolated muscle F/V relation is fitted by a well-known mathematical equation (7,11), but more interesting and useful is the “in vivo” relation and, more so, in a complex of muscular groups. Every motion, in fact, uses a coordinated action of different muscle groups, but not a single muscle contraction. So, the F/V curve morphology of squat exercises could be useful for characterizing the lower limb muscle complex of athletes, for both training programming and evaluating the effect of the training within a given time frame.

The study of squat F/V was the objective of Rahmani and Kellis (12,18). They reported an F/V relation of linear shape, which considered F and V as mean or peak values, but this timed type of analysis is not appropriate for evaluating force expression in complex multijoint movements, nor in isokinetic exercises.

Our starting hypothesis is that the F/V curve morphology of the motor complex of lower limb muscles, during a squat exercise, differs from the different load isometric contraction isolated muscle curves. Furthermore, the F/V relation analysis in real conditions could be very useful in the characterization of the muscle work in vivo and in the methodological preparation of motions undergone in sporting activities.

Moreover, we think that these shapes could be related to the muscular characteristics of athletes and could show some typical aspects of muscle fiber composition and the effects of training on them.

Therefore, the purpose of this study will be to analyze dynamic and kinematic parameters and their trends among the entire concentric phase of squat on well-trained track-and-field athletes for both endurance and resistance training. The aim of this work, then, is to integrate the information for the motion analysis and for more applications in training.

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Experimental Approach to the Problem

To obtain the most significant values, we chose to sensorize the Technogym “Multipower isotonic-line” in such a way to acquire displacement, velocity, and acceleration of the weight bar. The loads represent the independent variable and the bar displacement, velocity, and acceleration of the dependent variables. We considered bar velocity as the man-load system velocity, and we calculated the force with a model of the man-load system.

The constant load F/V relationship was obtained by force and velocity mean values of 10° angular intervals of the entire concentric squat phase.

A repeated-measures design was used to determine whether there were differences in curve shapes, at the various loads and among the subjects (resistance/endurance, men/women). The hypothesis, in fact, was that the shape of F/V relation could demonstrate differences in peak force expression time as a function of loads and of neuromuscular characteristics of any subject.

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Considering the purpose of the study, the choice of participants was fundamental. Not only must they be trained to correctly execute the CMS exercise at the maximal possible speed, but they must also show muscular characteristics as similar as possible among the groups (resistance trained men [RTM], endurance trained men [ETM], resistance trained women [RTW], endurance trained women [ETW]).

Twenty-nine subjects (15 men, 14 women) participated voluntarily in the study.

One month before the study, we collected data by different protocol settings and experimental designs on a separate group of subjects not related to this investigation. This allowed us to choose the protocol with the best compromise between data reliability and the possibility to perform all trials (to the 90% of 1RM) with the maximal intensity (speed).

The subject population consisted of 8 men (RTM) and 7 women (RTW) who practiced power discipline (racing speed), and 7 men (ETM) and 7 women (ETW) who practiced endurance discipline (long running), of track-and-field and participated in regional and national track-and-field competitions. They all had above 5 years of experience in agonistic competition. They trained 3-4 times per week with resistance training programs that included the squat exercise, and everyone was able to perform the countermovement squat (CMS) exercise correctly, as requested: flexion knee angle of 110° and maximal speed in eccentric and concentric phases. At the time of the study, all participants were at the same training period, after the indoor trials.

Age, anthropometrics measurements, and 1 repetition maximum (1RM) in 110° maximal knee flexion squat are given in Table 1.

Table 1

Table 1

Before beginning the study, the protocol was approved by the Ethics Committee of the University of Milan for use of Human Subjects. Participants were informed of the experimental risks, and they signed an informed consent statement.

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Squats were performed on a Technogym “Multipower isotonic-line” (4) connected with an incremental disc encoder (Minicod 5/12 B500R0C12).

The encoder is an electromechanical apparatus that allows the detection of the displacement of an object in the time. Once connected with the weight bar of the Technogym machine and with a specific software, it is possible to collect data about displacement, speed, and acceleration of the weight bar, and in first approximation, of the center of mass of the man-load system.

Encoder data were acquired by a PCMCIA National Instruments board (DAQCard-6024E) and collected by Preval (1.0) software and Biopac system (MP100). This acquisition system, developed, tested, and validated in collaboration with the Bioengineering Department of Politecnico di Milano was already used in some studies on movement analysis (13,16).

Hip and knee angle movements were registered by 2 surface electrogoniometers taped directly onto the skin. The knee sensor axis was well aligned to the sagittal axis of the femoral lateral epicondile.

The maximal knee flexion angles (110°) were attained when the subjects contacted the rear part of the thighs with a light elastic rope conveniently placed in the Technogym machine. We chose 110° as maximal knee flexion because we want to analyze the widest movement without imposing high knee intrajoint stress.

The hip sensor helped to control the postural asset during the exercise. Coordination between knee and hip movements was chosen as an index of correct exercise execution. The trial was considered correct when the movement inversions of the hip and knee were within a range of 10 ms and relative angles curves were both monotone decreasing function for the entire eccentric phase.

The experimental setup is shown in Figure 1.

Figure 1

Figure 1

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Experimental Procedures

Each subject performed 3 trials: In the first trial, they acquainted themselves with the exercise in the required way. In the second, after a standardized warm-up (10 minutes of treadmill run at 120-130 b·min−1 heart rate) the 1RM load was detected for the 110° squat with the 1RM direct method employed by Stone (20).

The third trial was after at least 2 days of recovery. The protocol, after warm-up, was 6 series of 1 CMS at maximal speed (eccentric and concentric) as possible with increasing load: 20, 35, 50, 65, 80, and 90% of 1RM load. Increasing load was preferred instead of randomized load to limit the possible effect of “postactivation potentiation” (6,8,9,19). The subjects were instructed to push the bar up as fast and as explosively as possible; they were not instructed to perform a jump during the concentric phase of squat, but if ground contact was not maintained during the effort, the measurement was still valid.

Recovery times, in accord with values in the literature (3,14), were 3 minutes for the first 3 loads (20, 35, and 50%) and 5 minutes for the other loads.

For the execution of the squats, subjects' heels were exactly on the vertical projection of the load bar with the same shoulder distance between the feet. This other parameter was slightly free because there are no data in the literature about the influence of feet distance on the parameters considered. A 3-cm heel board was used for those who could not stay with their heels on the floor for the entire range of motion (ROM).

Each subject always used the same posture chosen in the first trial. Starting and arrival postures were both with the knee totally extended (convention: full extension = 0°). Subjects looked straight ahead while they executed squats.

Immediately after a squat, the right execution was checked by electrogoniometer data. The exercise was performed correctly if the maximal knee flexion was between 105° and 115°, and if the inversion time was less than 10 milliseconds. For values outside this range, the hit was repeated after a 5-minute recovery. The trial was repeated also if the hip-knee coordination was out of the requirements as above or the speed was visibly valuable as not maximal.

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Statistical Analyses

The variables collected in a trial were as follows: displacement (cm), speed (m·s−1) and acceleration (m·s−2) of the bar, joint angles of knee and hip (°), knee angular speed (°·s−1), total force (N), and normalized force (NF = [F/(70%body weight + load)]).

Angle variables were acquired by the electrogoniometers at 200-Hz sampling rate, whereas linear values were registered by the Preval system at 50 Hz (Figure 2).

Figure 2

Figure 2

Displacements, speed, and acceleration are referred to the weight bar; the angular values are referred to the knee and hip articulations. Force values are calculated from the bar linear variables considering lower limbs as a single linear actuator. Internal forces were not considered.

To compare the subjects, force data were normalized by body weight and load, filtered (low-pass, 100-Hz, Butterworth filter), divided into eccentric and concentric phases and the concentric phase was fitted to obtain 100 values for each exercise.

The concentric phase was divided into angular intervals of 10° (obtained from knee electrogoniometer data) and, for each angular interval, we calculated mean and SD of all collected parameters. Constant load F/V relation was obtained by force and speed mean values of each angular interval: Considering the knee ROM as 110° for each load, the relation was designed by 11 points.

Statistical comparison of weight-bar NFs between men and women was performed with 2-sample unequal variance Student's t-test. The same t-test was helpful to compare, inside each group, the calculated parameters of the 2 intervals where the highest NFs were reached: 100-110° (movement inversion) and 40-30° (second peak).

One-way analyses of variance (ANOVAs 6 loads × 1 group, men or women) were calculated to determine the effects of the independent variables (loads) on the dependent variables (NF values at inversion-110°/100°-and second peak-40°/30°). When a significant difference was retrieved, post hoc Holm-Sidak method was applied.

Statistical significance was accepted at p ≤ 0.05. Results are expressed as mean ± SD.

Relative differences related to resistance and endurance trained athletes F/V curve morphologies were compared with the observation analytical method and not statistically.

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In the constant load F/V relationship, we observed differences in curve shape at varying loads, whereas there were no big morphological differences between men and women (Figures 3 and 4).

Figure 3

Figure 3

Figure 4

Figure 4

The force peak is reached in the inversion interval (V women = 0.2-0.3 m·s−1; V men = 0.3-0.5 m·s−1) in the first 4 loads. In 80 and 90% 1RM loads, the second peak (40-30°) prevails over the first peak (110-100°). In this angular interval, the velocity is 0.8-0.9 m·s−1 in the women's group and 0.9-1.1 m·s−1 in the men's group, respectively, for 90 and 80% loads.

Speed ranges change with load, decreasing when load increases (from 0.4 to 1.8 m·s−1 at 20% in the men's group and 0.3-1.4 in the women's group, to 0.1-0.8 and 0.1-0.9 m·s−1 at 90% for men and women, respectively).

Statistical comparison between inversion and second peak intervals in the men's group shows that, until 50% 1RM, the force values in inversion time are statistically higher; at 65% load, forces are the same; at 80 and 90% loads, the second peak is higher (p < 0.05) than inversion value acceleration (Figure 5).

Figure 5

Figure 5

Force values of 110-100° intervals were compared by a 1-way ANOVA for repeated measures (6 loads × 1 group, men or women), the same comparisons were made for 40°-30° interval to the changing loads.

In the first case, in the men's group, p was significant (p < 0.05) in relation to the load factor. This means that in the 110°-100° interval, force value clearly decreases with increasing loads.

In the 40-30° interval, there is not a statistically significant difference in the men's group among the various loads. Differently, what happens in the inversion interval where values continuously decrease, force expression between 40° and 30° increases in the first 3 loads and then it remains constant for the other loads.

In the women's group, the overtaking of force values in the last part of the concentric phase with respect to the inversion phase happens at 80% and 90% of 1RM. Statistical comparison between inversion and second peak intervals shows that, until 65% 1RM, the force values in the inversion time is statistically higher and at 90% loads, the second peak is statistically higher than inversion value acceleration (Figure 5).

One-way ANOVA shows that, as for the men's group, p is significant (p < 0.05) for the load factor, in both the angle intervals (110-100° and 40-30°). In fact, in this group, force value increases with loads until the last load.

The comparison between resistance and endurance trained athletes showed that, in the men's group, the RTM athletes reached higher force values than did the ETM group at all loads and above all at second peak time (Figure 6). In the women's group, the RTW athletes exhibited major values than did the ETW group at inversion time but not at second peak time (Figure 7).

Figure 6

Figure 6

Figure 7

Figure 7

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Constant load F/V relationship in the squat exercise does not follow a linear shape; it does not have an equivalent criterion among all loads.

In fact, although lower load forces decrease with increasing speed, with higher loads, an increment in force values with increasing speed is observed, although the velocity value range is narrower.

So, a force peak is developed in different moments of the concentric phase with the variation of the load.

Till 65% of 1RM, Fmax is expressed in the inversion moment (110-100°) when the speed is minimum. To the contrary, at 80 and 90% of 1RM, Fmax is reached in the final phase of the rise (40-30° range).

In this range, the linear speed of the weight bar reaches the maximal values. Obviously, it decreases relative to the increasing load.

This was already observed by Zink et al. (21), who described a “second peak” during the concentric phase of the “half-squat” exercise; furthermore, the movement of the weight bar, in correspondence to to the “first peak” (inversion phase) is almost zero, whereas the second peak agrees (in time) with the top of the power curve and is related to the maximal linear speed.

Factors that contribute to this phenomenon are partially related to the muscle physiology and to the geometry of the joints involved in the motion.

The inversion phase force is expressed in near-isometric condition, and it can be considered quite constant with respect to the load changing, too, because the inertial mass is always the maximal endurable load. In fact, when the weight is low, the subjects arrive at the inversion phase with a high speed; this causes a similar total work compared with the need to stop a high load that moves at lower speed.

For this reason, it is possible to consider that the contractile component of the force is maximal at every load. Many important variables at the base of the small variation with respect to this phenomenon are those related to the countermovement act, elastic energy storing, neuromuscular nature, coordinative and engagement of motor units.

The highest descending speed reachable with low loads, in fact, can cause an increase in both neuromuscular activation and muscular-tendon system stiffness with a decrease in coupling time and a reduction in thermal dispersion energy (2).

Considering the First Dynamic Law (F = m × a), we know that the inertial mass increases with the raised weight. Because F, as mentioned before, is almost constant, “a” decreases in an inversely proportional manner with respect to “m.”

At the end of the concentric phase, instead, it is clear that acceleration does not decrease, but more so it tends to increase, until it reaches a peak (40-30° range) that exceeds the value registered in the inversion phase.

The hypothesis about the “second peak” is based on the differences in velocity in this range related to the loads. As the linear speed in the concentric phase goes down when the load increases, the athlete reaches the last push phase in a condition much better for the force expression, and so, he can create a higher acceleration with respect to what he can achieve with the low loads.

Because the physiologic F/V curve has a hyperbolic shape, close to the isometric condition, for small differences in linear speed, we have big changes in force. In the 40-30° range, speed is highly related to the single exercise, but really lower then muscle maximal contraction velocity. In fact, absolutely low velocities are involved in this exercise, and the situation corresponds to the high part of the physiological F/V curve, so the increase in expressed force is always proportionally higher than the increase of the inertial mass. From this, in relation to F = m × a, acceleration also increases.

Probably, the second peak is observed in this range (40-30°) and not before, because in this range we find, in addition to the maximal effect of the angular speed variation, the influence of the increased arm of the angular momentum of the knee. In the knee joint, the instant center of rotation moves with the joint angle. The results are minimal when the joint is flexed and maximal near 50-40° of flexion.

Also, the muscular force shape of the femoral rectus is involved: In fact, although the vastus muscles have the peak torque near 90° of flexion, rectus (2 joints related) reaches its maximum force as knee extensor, in the final part of the raise, when the trunk is vertical (5).

With physiological and geometrical factors, the relation between linear displacement of the weight bar and angular knee velocity can motivate the movement of the acceleration peak in relation to the load.

Linear displacement of the weight bar during the squat exercise is a product of angular movement of the joints involved (mainly the knee joint). At the inversion phase, when the knee is flexed, every little angle change produces a large displacement in the height of the bar. With knee extension, every angular range will produce a little bar displacement that is also reflected in knee angular (VAG) and bar linear (VL) velocity. As a consequence, the knee extension velocity must increase more and more to reach a constant weight-bar linear speed.

The ratio between angular and linear motion changes along the different angular ranges. In real motion, even if there are small deviations from the geometrical relation between VAG and VL, in the same angular range, linear velocity of the weight bar decreases with increasing loads. This decrease is higher in VAG; differences between minimum and maximum loads in the second peak range are 85°·s−1 in men and 114°·s−1 in women. This means a significant movement to the higher part of the theoretic F/V curve and consequently an increase in the capacity of force expression.

Moreover, there is the ratio effect caused by the angular/linear relation that allows raising the same load with less joint torque. Thanks to this, in the last degree of the concentric phase, it could be possible to maintain the same linear bar speed with less knee (and hip) torque. But, because the exercise has to be done at as high a speed as possible till the end of the complete knee extension, joint torque did not decrease with linear weight-bar acceleration increase in this angular range.

Other than the change in the moment of the peak force, we observed the morphology of the entire F/V curve along the concentric phase related to the loads.

On splitting the subjects into 2 groups in based on typology of disciplines practiced (resistance and endurance), the same frequent characteristics in the curve shape were noticed, in both the men's and women's groups.

Resistance trained men reach strength values higher than ETM subjects. Resistance trained men athletes, evidently, are able to exhibit a high ratio of strength and to maintain the same level at high speed.

In fact, these subjects show a “second peak” definitely higher and larger with respect to that observed in ETM athletes. In this group also, the range of speed is wider in the concentric phase.

In RTW athletes, it is possible to observe higher strength values with respect to the ETW group only in the inversion phase: The 2 groups have similar values in correspondence to the second peak.

Resistance trained subjects seem to better take advantage from elastic and coordinative factors during the inversion phase, when speed is near zero, but they cannot maintain their strength when the speed increases. Differences between men and women can be related to hormonal factors. According to Bosco (1), concentration of testosterone could enable an improvement of explosive force and speed.

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Practical Applications

On the strength of this study results, the morphological examination of the whole curve could be useful to check and to identify muscle characteristics of athletes, for training scheduling and to evaluate training effects in the long run (longitudinal control).

To obtain the best performance in a specific move, it is common to train at the typical speed of that move. But in reality, it is difficult to know how much strength the athlete is able to express at this typical speed. Once we know the joint angles and the speed needed, this method can easily provide the answer: how much force an athlete can express at that speed.

Also, a programmed examination of F/V curves could easily clarify doubts in training programs. Athletes, are often able to mask the real training results thanks to technical improvements or great emotional motivation. So, the risk in losing time in not appropriate training is effective. The monitoring of F/V curves could decrease this risk with an objective control of the muscle capacity of the athlete.

With time, it will be possible to create discipline-specific databases: This could allow athletes' potentiality evaluation and could give an index to rationalize disciplines and objective choice in the most appropriate direction for the athlete.

In addition, this method could be useful in monitoring the postinjury recovery training like the vertical jump dynamic analysis can.

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We are grateful to the Department of Sport Sciences, Nutrition, and Health for use of instrumentation and laboratory and to Vibram and its Tester Team for their support. The authors disclose professional relationships with companies or manufacturers who benefit from the results of the present study. Results of the present study do not constitute endorsement of the product by the authors or the NSCA.

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squat; encoder; lower limbs

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