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On the Effectiveness of Force Application in GuidedLeg MovementsCaroline A. M. Doorenbosch a , Dirkjan H. E. J. Veeger a , Jan Peter van Zandwijk a & GerritJan van Ingen Schenau aa Institute of Fundamental and Clinical Human Movement Studies Vrije UniversiteitAmsterdam , The NetherlandsPublished online: 01 Apr 2010.

To cite this article: Caroline A. M. Doorenbosch , Dirkjan H. E. J. Veeger , Jan Peter van Zandwijk & Gerrit Jan van IngenSchenau (1997) On the Effectiveness of Force Application in Guided Leg Movements, Journal of Motor Behavior, 29:1, 27-34

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Journal of Motor Behavior, 1997, Vol. 29, No. 1, 27-34

On the Effectiveness of Force Application in Guided Leg Movements

Caroline A. M. Doorenbosch DirkJan (H. E. J.) Veeger Jan Peter van Zandwijk Gerrit Jan van lngen Schenau Institute of Fundamental and Clinical

Human Movement Studies Vrije Universiteit Amsterdam, The Netherlands

ABSTRACT. In guided leg movements (e.g., in cycling or wheelchair propulsion), the kinematics of a limb are determined by the object on which a force is applied. As a consequence, the force direction can vary and may deviate from the movement direction, that is, the effective direction. In the present study, the relation of effective force application and maximal power output was exam- ined. Subjects (n = 5 ) performed guided leg tasks on a special dynamometer. They were instructed to exert a maximal force against a moving forceplate in the direction of the movement, as if they were pushing the plate away. Three different movement directions were tested: perpendicular to the horizontal, rotated 30" backward, and rotated 30" forward. For each trial, force and position data were recorded. The results of the experiments showed that in the extreme movement directions (both 30' conditions), the force vector deviated significantly from the direction of the movement. Apparently, maximal power output was achieved with a low force effectiveness in these tasks. The background of this phenomenon was revealed by using the kinematics of one of these tasks in a simulation model. The stimulation level of 6 leg muscles was optimized toward a maximal effective force component (a) without a constraint on the direction of the total force or (b) with a constraint on the force component perpendicular to the effective force. The muscle stimulation pattern that resulted in the highest effective force coincided with a low force effectiveness. Apparently, this is a prerequisite for maximal power transfer from the muscles to the plate in these guided movements.

Key words: contact control, force control, force effectiveness, humans, leg tasks

he problem of how the central nervous system controls T all the degrees of freedom of the musculoskeletal system so that motor behavior can be harmonious and functional is a major issue in the various disciplines that consti- tute the human movement sciences. In spite of the seemingly infinite number of possibilities, different

(skilled) subjects execute a particular motor task with little variation (Ingen Schenau, 1989). This suggests that there are structural or functional constraints that limit the set of possible movement and activation patterns.

The so-called guided movements are a specific type of complex movements. In guided movements, the trajectory of the foot or hand is determined by the object on which a force is applied, as, for example, is the case during cycling and wheelchair propulsion. In contrast to a free movement along a predefined trajectory (Miller, Gielen, Theeuwen, & Doorenbosch, 1992; Theeuwen, 1994), the direction of the pushing force during a guided movement is not prescribed.

It has often been argued that, from a mechanical point of view, the force should be directed in the direction of the movement because, in that case, the total force will contribute to the work needed to accomplish the task. Deviation from this direction would mean that part of the exerted force does not contribute to the external work. The latter is con- sidered to be ineffective (e.g., Davis & Hull, 1981; Ericson & Nisell, 1988; Faria, 1992; Zschorlich, 1989).

Remarkably, measurements of forces in handrim wheelchair propulsion (Roeleveld, Lute, Veeger, Gwinn, & Woude, 1994; Veeger, Woude, & Rozendal, 1991a, 1991b) and in cycling (Coyle et al., 1991; Davis & Hull, 1981; Ericson & Nisell, 1988; Faria, 1992; Hull & Davis, 1981; Ingen Schenau, Boots, Groot, hackers, & Woensel, 1992;

Correspondence address: Caroline A. M . Doarenbosch, D- epartment of Rehabilitation, Free University Hospital, Vrije Uni- versiteit, PO. Box 7057, 1007 MB Amsterdam, The Netherlands. E-mail address: [email protected]

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C. A. M. Doorenbosch, H. E. J. Veeger, J. P. van Zandwijk, & G. J. van lngen Schenau

Lafortune & Cavanagh, 1983; Redfield & Hull, 1986a, 1986b) have shown that subjects do not apply the propul- sive force in line with the trajectory of the hand or foot. In cycling, the ratio of effective force to total force, referred to as pedal force effectiveness (Faria, 1992), did not appear to be larger than 76% for elite cyclists. Faria (1992) used the term wasted force suggesting that the force component in the direction of the crank axis is wasted. However, in experiments aimed at increasing the effectiveness of the exerted force by using feedback during cycling, higher power out- puts on the pedal did not occur (Faria, 1992; Lafortune & Cavanagh, 1983).

As argued before (Ingen Schenau, Koning, & Groot, 1994), the force component in the direction of the crank axis is not necessarily associated with any waste of meta- bolic energy. Rather, pedal force effectiveness is related to the force and work distribution among the hip and knee extensors. Apparently, muscle coordination during these guided movements results in a seemingly ineffective force component on the pedal or wheelchair rim.

Our aim in this study was to illustrate why the phenomenon of such an ineffective force is the most optimal with respect to the goal of the (standardized) guided leg tasks, that is, maximal power output. We will demonstrate that power output is not related to force effectiveness.

To get insight into the underlying muscle coordination pattern, one of the tasks was simulated with a model of the lower extremity by optimizing the muscle stimulation of each modeled muscle to a maximal effective force component.

Method

Subjects

Five healthy subjects (1 woman and 4 men; aged 29 k 2 years; height, 1.81 f .03 m; weight, 74.8 f 6.4 kg) partic- ipated in the experiments.

Protocol

The subjects were seated in a dynamometer on a bike sad- dle, such that the right foot was placed on the forceplate (Fig- ure 1). The dynamometer consisted of a rail along which a forceplate could move in a straight line over 1 m, placed within a frame. The rail could be mechanically rotated about an axis at the lower side of the rail as well as translated over a double bar at the bottom of the frame (see arrows in Figure l), which allowed adjustment of different movement directions. The movement of the forceplate was controlled by a servo-motor (SEM, MT30U4-36, London, Great Britain) via a ball-rotation spindle, using a motion control software pack- age (GALL DMC-710, Sunnyvale, CA).

Subjects were first placed in a reference position, with the hip angle at 1 15" and a knee angle of 100" (for both joints, 180" is full extension). The ankle angle differed, depending on the position of the forceplate. Before the actual experiments started, anthropometric parameters were obtained from each subject.

FIGURE 1. Outline of the dynamometer. The right foot of the subject was placed on a forceplate, which moved in an up- and downward direction along a rail. The rail could be rotated and translated (see arrows) so that different movement directions could be obtained.

During the experiments, subjects were instructed to exert a maximal force in the movement direction of the moving forceplate, as if they were pushing the plate away. No movements of the foot relative to the forceplate were allowed. Three different movement directions were imposed: one in which the forceplate moved away from the subjects in a downward neutral direction ($ = 0), one in which the rail was placed in a 30" forward position (Q = -30), and one in which the rail was rotated 30" backward ($ = 30) (see Figure 2). In each movement direction, the tasks were executed under isokinetic conditions at four different velocities of the forceplate: 10, 20, 30, and 40 c d s , resulting in 12 different tasks. Additionally for each subject, 1 of the 12 tasks was randomly chosen and repeated five times.

For all trials, the forceplate was positioned 20 cm higher than the standard position. A 1.25s period was used for placing the foot on the forceplate and exerting a force on a stationary forceplate. Thereafter, the subjects had to exert a maximal force while the forceplate moved downward with a fixed velocity until it was 20 cm below the standard position. For all tasks, a trajectory of comparable joint angles was passed. Total movement time for the isokinetic trials differed for each velocity.

For each protocol, we used computer-generated audible signals to indicate the start of the trial, initiation of the movement, and end of the trial. These signals were simulta-

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30 0 - 30

FIGURE 2. Illustration of the three movement directions of the forceplate used in the experiments. Vertical position is indicated at O", backward at -30". and forward at 30". Sub- jects were instructed to exert a maximal force while the forceplate moved in the direction of the arrow.

neously recorded as block pulses and used for synchroniza- tion in time. On each trial, joint position and reaction force were recorded.

Position and Force Markers (13 mm diameter) placed on the skin corre-

sponded with the fifth metatarsophalangeal joint, heel, lateral malleolus, knee joint (on the lateral collateral ligament at the height of the knee cleft), greater trochanter, top of iliac crest, and neck (at the height of the fifth cervical ver- tebra). Two markers were placed on the forceplate and three on the dynamometer frame as a reference orthogonal coor- dinate system.

The displacements of the right leg were collected at 60 Hz, using a motion analysis software system (VICON, Oxford Metrics Ltd., Oxford, Great Britain). With the VICON system, three-dimensional coordinates were calculated. After proper scaling, the absolute coordinates of the anatomical landmarks in the sagittal plane were obtained and subsequently low-pass filtered (zero phase lag, net cut- off frequency 2 Hz). We chose this low cut-off frequency to minimize quantitization noise; it was adequate in these rela- tively slow isokinetic movements because the joint angles and their derivatives did not contain higher frequencies than 1 Hz. The coordinates defined four body segments: foot, lower leg, upper leg, and a part of the upper body, which we used to calculate joint angles as well as joint velocities (Lanczos, 5-point differentiation filter; Lees, 1980). To determine the positions of the mass centers of the different body segments, we combined the coordinates with anthropometric measurements and data from Clauser, McConville, and Young (1969) and Winter (1 979).

The reaction forces of the right foot were recorded by means of strain gauges built in a forceplate. The analog force signals were amplified, low-pass filtered (75 Hz, 24 dB/oct), and sampled (600 Hz, 12 bits) by the VICON system. From the distribution of the separate force components, the center of pressure of the force vector was calculated. Combined with the points of reference of the position data, the center of application was related to the position of the foot.

We applied Newtonian equations of motion to a linked segment model of the human body in order to calculate the net torques about the hip and knee joints (Elftmann, 1939). Hip and knee extension torques were defined as positive.

Data Analysis

For each trial of each subject, the values of several vari- ables (e.g., reaction force) were calculated over the period in which the foot displacement was within 5 cm of the reference position. Next, the mean values of this time period were calculated for each trial. Subsequently, for all subjects, these values of the corresponding tasks were averaged.

To test for possible differences that may have resulted from movement velocity or movement direction, we performed a two-way analysis of variance (ANOVA), with repeated measurements (a probability level I .05 was con- sidered to be statistically significant).

Musculoskeletal Model The musculoskeletal model used for the simulation of a

guided leg task included two parts: the skeletal and the muscular model (MUSK system; Casius, 1995). The skeletal part, representing the lower extremity, was modeled as a planar system consisting of three rigid segments: thigh, shank, and foot. At the toe, the skeletal system was con- nected to a movable plate, and the hip was fixed as the most proximal joint. Segmental parameters were obtained from the measurements of 1 of the subjects. The muscular part of the model consisted of Hill-type muscle models, which have proven to give a satisfactory description of the muscle behavior in the context of gross motor behavior (Hatze, 1981; Soest, Huijing, & Solomonow, 1995; Winters 1990). All parameters and definitions used for this general purpose Hill-type muscle model are described in detail in Soest et al. (1995) and Casius (1995). Input to the muscle model is stimulation, a representation of recruitment and firing rate of a-motoneurons, ranging between 0 and 1; output is muscle force. Muscle groups incorporated in the musculoskeletal model were representations of the gluteus maximus, hamstrings, vasti, rectus femoris, soleus, and gastrocnemius muscles. In the simulations, the experimental kinematics of 1 of the subjects in direction 41 = -30 at velocity 20 cm/s was used as input. Subsequently, muscle stimulation was optimized for each of the two performance criteria. The input, which is the stimulation level [0 + 13 of each muscle, determined the contribution of the muscle force to the output of the model, that is, the ground reaction force vector. For the

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simulation, we adjusted the stimulation patterns of the six muscles to maximize the force component in the direction of the movement (effective force) under one of the following different conditions: (a) Maximize the effective force without constraints on the other force components or (b) maximize the effective force with a constraint on the component perpendicular to the effective force (shear force).

Results For each subject, the individual coefficients of variation

of force magnitude and direction were calculated from the randomly chosen condition, which was repeated five times, and expressed as a percentage of the mean value of these trials. These percentages were below 5% for both magnitude and direction.

No significant differences were found between the exerted maximal force for the different tasks @ I .05), which means that the velocity of the forceplate and the movement direction did not have a significant effect on the magnitude of the exerted force. The overall averaged force magnitude was 830 N (SD f 141). The velocity did not have a significant effect on the direction of the force either, whereas the movement direction did @ I .05). A post hoc 'hkey test revealed that only the force exerted in movement direction Q, = -30 differed significantly from those exerted in movement directions Q = 0 and Q, = 30.

The ranges of the direction of the force are contained in Table 1. Force direction values were defined in correspondence with the movement directions; that is, 0" was perpendicular to the horizontal. The data reflected the averaged minimum and maximum force directions of all subjects for the trajectory where the foot was within 5 cm of the reference position. With the mean force direction exerted in that trajectory, the deviation of the force vector from the direction of the movement ($) of the forceplate was obtained. The mean absolute deviation for Q = 30 was 35.6" (k 3.9); for Q = -30, 33.4"(* 2.6); and for Q = 0, the absolute deviation was 4.7" (+ 2.8). This indicated a force effectiveness of only 81% and 83% in movement directions 30 and -30, respectively.

I TABLE 1

Range of Force Direction (in Degrees Relative to the Horizontal) for Each Condition Separately

Movement Movement condition velocity ( cds ) 30" 0" -30"

10 20 30 40

2.9-8.2 3.0-5.8 0.1-5.5 5.6-9.3 3.8-6.0 0.8-4.9 3.7-7.7 3.5-5.6 1.5-6.9 2.54.5 3.5-6.3 1.8-6.2

Note. Values of force direction were obtained &om the movement trajectory in which the foot was within 5 cm of the reference position. The data reflect the maximum and minimum values of the mean data of all subjects for each corresponding task.

The stick figures in Figure 3 show the movement pattern and the executed force of 1 typical subject for the tasks at a 2O-cds velocity. From left to right, the figures correspond to the movement directions 30, 0, and -30, respectively. Total movement time was divided into 3 intervals. These are shown by the different stick figures for each task. The force vector shows the direction and magnitude of the reaction force that was actually executed. An important observation was that the reaction force was mainly directed between the hip and the knee for all different conditions.

Evaluation of Model Output Figure 4A shows the results of the computer simulations.

The foot on the plate moved downward in the -30 direction for 2 s (velocity 20 c d s ) . The output of the model, which was the reaction force vector, is shown for both optimization criteria. The vectors in the left diagram show the direction and magnitude of the reaction force for Condition 1 (no constraints), and the right plot shows the reaction force vector of the model for Condition 2 (minimal shear force). As can be observed, the force magnitude was about 3 times larger in the 1st condition than in Condition 2. The optimized muscle stimulation levels that led to these reaction forces (Figure 4A) are shown in Figure 4B for both conditions. All the muscles that were activated operated at hgh to maximal levels. For the constrained condition, only the hamstrings and gluteus were maximally stimulated, which resulted in a reaction force that was directed in the effective direction. For the unconstrained condition, almost all modeled muscles were activated, resulting in a force vector that deviated from the direction of the movement but had a higher effective component than the force vector in Condition 2.

I FIGURE 3. Stick figures show the movement pattern and the executed force of a typical example for the experimental task at 2O-cds velocity. From left to right, the figures correspond to the movement directions 30". 0", and -30", respectively. Total movement time was divided into three intervals. These are. shown by the different stick figures. The force vector shows the direction and magnitude of the reaction force. The arrows show the movement direction of the forceplate.


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E 0 2

OPTIMIZATION CONDITION 1

GU HA RF VA GA SO muscles

OPTIMIZATION CONDITION 2

0.4

0.2

I

GU HA RF VA GA SO muscles

FIGURE 4. A. Stick figures show the three segments, thigh, shank, and foot, which were used for the simulation of the guided movement in direction -30 for the 2 0 - c d s velocity. The left stick diagram shows the reaction force vectors obtained with the model for Con- dition 1 (no constraints on force direction), and the right stick figure shows the same data for Condition 2 (shear force constrained). The arrows show the movement direction of the forceplates. B. Optimal muscle stimulation levels for each of the six muscles (GU, gluteus maximus; HAM, hamstrings; RF, rectus fernoris; VA, vasti; GA, gastrocnemius; and SO, soleus). Stimulation could vary from 0 to 1 (maximal). Left and right plots show optimization Conditions 1 and 2, respectively. Each bar indicates the level of stimulation obtained after optimization.

Discussion

Control of Force Direction It has often been stated that in guided movements, the

force vector should have a direction that corresponds to the movement direction (e.g., Faria, 1992; Lafortune & Cavanagh, 1983; Veeger et al., 1991a; Zschorlich, 1989, 1992), because the force would then contribute optimally to the external work. Studies in which the force was actually measured have proved this assumption to be wrong: Subjects Qd not apply the external force in the mechanically most effective direction (Coyle et al., 1991; Faria, 1992; Ingen Schenau et al., 1992; Redfield & Hull, 1986a, 1986b; Roeleveld et al., 1994; Veeger & Woude, 1994). Furthermore,

for the guided leg tasks in the present study, the forces were not applied in line with the trajectory of the foot. The results of these experiments clearly demonstrated that, despite the instruction to apply the force in the movement direction of the platform, all subjects directed the force vector between the hip and knee, irrespective of movement direction. Although the gravitational force on the leg was only about 1 1% of the mean external force of 830 N, gravity can explain only a minor part of this phenomenon.

Although, intuitively, a low force effectiveness may be associated with a low contributory force (e.g. Faria, 1992; Zschorlich, 1989), one can use a power balance model of the leg to help prove that this intuition is wrong. In fact, the force component perpendicular to the movement direction

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(shear force) does not have any significant influence on power output as long as a significant force component is present that can do work on the plate (effective force com- ponen t) . Force Effectiveness and Power Output

As originally deduced by Aleshinsky (1986a, 1986b) and applied to cycling by Ingen Schenau, Woensel, Boots, Snackers, and Groot (1990), the power equation of the combined three leg segments for the dynamometer tasks equals

(1) where Ti and wi are the net torques and angular velocities of the joints involved. The terms F, and v, represent the external force vectors (here, the force exerted on the forceplate and the net hip joint force) and the velocities of their points of application; dUdt is the rate of change of potential, kinetic, and rotational energy of the leg segments. The contribution of the hip joint force is small (Ingen Schenau et al., 1990), which means that CF, 0 v, largely reflects the power transfer from the foot to the forceplate.

The scalar product of the force on the forceplate F, and the velocity of the forceplate v, again might suggest that power output P, = F, 0 v, cos 8 (with 8 the angle between F, and v,) is maximal with a force effectiveness of 100%. The power equation demonstrates that this is not the case, however. Because the angular and translation velocities as well as dWdt are fixed as a result of the imposed movement trajectory and velocity, the largest power output (F, v,) is achieved by optimizing the sum of joint powers (ZT,wi),

CTia = C F, V, + dE/dt,

A B

FIGURE 5. A. Illustration of the actual exerted force in movement direction -30 during the experiments. B. Illus- tration of a maximal effective force, with a similar magnitude of the vector as in A. The dashed lines show the lever arms of the hip and knee. In comparison with the situation in A, a hip extending torque more than twice as great and a significant knee flexion torque would be required in the situation in B.

regardless of the angle between F, and v,. Actually, in these tasks where the angular velocity w is prescribed, the power output is determined by optimizing the sum of joint torques (W.

So that this theoretical evidence against the significance of force effectiveness can be understood, a simple example may assist in giving an impression of the relation between force effectiveness and joint torques. On physiological grounds, for the guided leg tasks with given joint extension velocities, the maximal deliverable net torques about the joints are assumed to be the major constraint. A consequence of this assumption can be illustrated with the aid of an example of the task with movement direction -30. The actually realized reaction force is shown in Figure 5A (left). Imagine that someone manages to increase the effectiveness of the force by exerting a force in the direction shown in Figure 5B (right). Obtaining the same force magnitude in 5B as the one shown in 5A would require a hip-extending torque more than twice as large and a significant knee flexion torque, resulting in an improvement of the power output. Based on physiological considerations, however, this is highly unlikely to occur. It implies an increase of more than 100% in the force and power output of the hip extensors (e.g., hamstrihgs and gluteus maximus) at the same contraction velocity. When the hip extensors are already per- forming at their optimal force or power output, the hip torque most likely remains the same. As a consequence, this would result in an external force (F,) of about half the value of Ft in the situation shown on the left. Moreover, the real- ization of a net flexion torque about the knee in Figure 5B requires an additional increase in force of the main knee flexors, the hamstrings. We assumed, however, that the output of these muscles was already maximal. This would mean that the requirement for a flexion torque about the knee could be realized only by inactivating the knee extensors. At the given contraction velocities, this would lead to a lower power output compared with the situation in which force effectiveness is lower. Because the kinematics and gravity are equal in both situations shown in Figure 5, the neglect of inertial and gravitational influences in the example does not affect this reasoning. Therefore, a coordinative pattern of the involved muscles obviously results in a force vector that may seem ineffective but, in fact, appears to be aimed at maximizing the power output. Attempts to optimize the force effectiveness, as described, for example, by Faria (1992) and Zschorlich (1989), will therefore result in lower external forces, such that the external power will decrease.

Muscle Coordination Given the patterns of activity found in cycling and other

leg tasks, as well as during manual wheelchair propulsion, the variations of the direction of the external force are lim- ited largely by the capacity of the muscles to distribute the net torques about the joints. For this reason, force direction in repeated leg extensions with a line of action far behind the hip or far in front the knee are seldom observed. These


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types of movements are apparently controlled by finding an optimum between muscle power output, on the one hand, and a reasonable effective force component, on the other. This was also demonstrated by the simulation results in which optimal power output was found by using two different criteria: (a) maximizing the effective force component, with no restrictions on the component perpendicular to the movement direction (shear force); and (b) maximizing the effective force component, with minimal shear force.

The results of the simulation (Figure 4) have demonstrated that optimal power output is not related to force effectiveness and support the ideas elucidated above. For a maximal power output, all contributing muscles were activated at a high or maximum level. Thus, constraining the shear force and maximizing the effective component could be realized only by inactivating some of the muscles (see Fig- ure 4B). This resulted in a much lower force and power output compared with that of the unconstrained condition. As a consequence, a higher effectiveness went hand in hand with a lower power output. Apparently, the simulated muscle activation pattern also produced a force component perpendicular to the movement direction, which neither contrib- uted to nor retarded the motion. For maximal effective force and, as a consequence (at similar velocities), maximal power output, the shear force component should be nonzero. This agrees well with the presented experimental results and also occurs during cycling and manual wheelchair propulsion. The practical consequence is that improvement of work output through improvement of force effectiveness is a fallacy. This conclusion is supported by studies on the improvement of force application in cycling (e.g., Lafortune & Cavanagh, 1983).

ACKNOWLEDGMENTS This study was supported by the Life Sciences Foundation,

which is funded by the Netherlands Organization for Scientific Research (NWO). The MUSK system was available with the financial support of Cray Research Inc.

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Submitted October 20, 1994 Revised August 9, 1995

Second revision February 26, 1996

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