Support for mechanical advantage hypothesis of grasping cannot be explained only by task mechanics

ABSTRACT Successful object interaction during daily living involves maintaining the grasped object in static equilibrium by properly arranging the fingertip contact forces. According to the

mechanical advantage hypothesis of grasping, during torque production tasks, fingers with longer moment arms would produce greater normal force than those with shorter moment arms. Previous

studies have probed this hypothesis by investigating the force contributions of individual fingers through systematic variations (or perturbations) of the properties of the grasped handle.

In the current study, we examined the validity of this hypothesis in a paradigm wherein the thumb tangential force was constrained to a minimal constant magnitude. This was achieved by

placing the thumb on a freely movable slider platform. The total mass of the handle was systematically varied by adding external loads directly below the center of mass of the handle. Our

findings suggest that the mechanical advantage hypothesis manifests only during the heaviest loading condition when a threshold difficulty is reached. We infer that the support for the

mechanical advantage hypothesis depends not only on the physical parameters but also on the individual ability to manage the task. SIMILAR CONTENT BEING VIEWED BY OTHERS EVIDENCE TO SUPPORT

THE MECHANICAL ADVANTAGE HYPOTHESIS OF GRASPING AT LOW FORCE LEVELS Article Open access 02 December 2022 DISTINCT SENSORIMOTOR MECHANISMS UNDERLIE THE CONTROL OF GRASP AND MANIPULATION

FORCES FOR DEXTEROUS MANIPULATION Article Open access 25 July 2023 DISTINCT BEHAVIOR OF THE LITTLE FINGER DURING THE VERTICAL TRANSLATION OF AN UNSTEADY THUMB PLATFORM WHILE GRASPING Article

Open access 26 October 2021 INTRODUCTION Among all the activities of daily living, grasping and manipulating objects is one of the most crucial and fundamental actions performed by humans.

Maintaining the grasped object in static equilibrium is perhaps a critical aspect that governs safe handling by avoiding clumsy behavior such as dropping and spilling. Any form of

perturbations to the grasped object requires a complete rearrangement of the fingertip forces to sustain the static equilibrium. Previously, studies have been performed to investigate the

force contribution of the individual fingers and thumb when systematic variations (or perturbations) were imparted to the properties of the grasped handle. Such variations involved

introducing external torques1,2,3,4, varying the mass of the external loads5,6, surface friction modification7,8,9, alteration to the grip width of the handle10 or individual digit width11

in the horizontal direction, and change in the position of the fingertips12 and the thumb3 while grasping. Normal and tangential forces of the individual fingers and thumb varied

systematically in response to these perturbations. Some of these perturbations also disturbed the rotational equilibrium of the handle. In such situations, compensatory torque production was

required by the fingers to sustain the handle in static equilibrium. Considering the position of the thumb as pivot point (located midway between middle and ring finger) while grasping a

handle, peripheral fingers (index and little) have longer moment arm for normal force than the central fingers (middle and ring) with shorter moment arm for the normal force. According to

the mechanical advantage hypothesis (MAH)13,14, during compensatory moment production tasks, for example, when there is a requirement to produce supination moment (or torque) in the

clockwise direction, little finger with longer moment arm for normal force tends to produce greater normal force than its neighboring ring finger with shorter moment arm for normal force.

Thus, by utilizing the mechanical advantage of the little finger, the total force produced by the ulnar fingers could be reduced without compromising on the required moment15. Several

studies have attempted to examine the validity of the principle of mechanical advantage for a five-finger grasping task. Mechanical advantage hypothesis was supported in tasks that involved

handle rotation in the pronation and supination directions at two different speeds16, the addition of an external load of different masses at varying distances from the center of mass of the

handle17, and moment production to follow a trapezoid template by pressing with all four fingers18. However, the hypothesis was only partially supported in a moment production task on a

mechanically fixed object19, where the distance from the fingers to the axis of rotation, magnitude, and direction of torque production was varied systematically. The authors of the

afore-mentioned study posited that the applicability of the MAH may be task and effector-specific. As such, it is yet unclear what kind of tasks the applicability of MAH depends on.

Therefore, it is necessary to investigate whether the applicability of mechanical advantage is task-specific and which kind of tasks/scenarios support the MAH. In our previous study20, we

had attempted to investigate the applicability of MAH by introducing torque changes to the handle. Rather than implementing external torque changes by suspending the load at a distance from

the center of mass of the handle, we incorporated the torque changes by reducing friction between the thumb platform and the handle interface. This was made possible by placing the thumb on

a slider platform that could freely translate vertically over a railing. In this way, the tangential force produced by the thumb was kept constant and less than the virtual finger21 (an

imaginary finger whose mechanical output is equal to the combined output of the individual fingers except for the thumb). This had resulted in introducing a residual pronation torque to the

handle. Since the instruction was to maintain the handle in static equilibrium, a compensatory supination torque was required to avoid the tilt caused as a result of the residual pronation

torque. Ulnar finger normal forces and thumb tangential forces are major contributors to this compensatory supination torque. However, by our design, it was not possible to increase the

tangential force of the thumb as it had to hold the slider platform steady at the HOME position (midway between middle and ring fingers). Therefore, only the normal forces produced by the

ulnar fingers became the primary source of this compensatory supination torque. Between the ulnar fingers, the little finger has a larger moment arm for normal force when compared with the

ring finger. Hence it was expected that the little finger would produce greater normal force. Contrary to this expectation, ring and little fingers were found to share comparable normal

forces while grasping the handle of mass 0.535kg20. Therefore, in the current study, we expected that MAH would be corroborated if the mass of the handle is increased systematically by

adding different external loads. As per the design of this grip device, the tangential force of the thumb was constrained to a constant minimal magnitude. So, with an increase in the mass of

the handle, only the tangential force of the virtual finger increases, which is accompanied by an increase in the residual pronation torque. As a corrective effect, the magnitude of

compensatory supination torque required to be produced would also increase. Hence, we expected that with a systematic increase in the mass of the handle, the little finger would produce

correspondingly higher normal force than the ring finger during compensatory supination torque production. In line with such an expectation, in the current study, the mass of the handle was

systematically increased by employing external loads of mass 0.150, 0.250, 0.350, and 0.450 kg as different experimental conditions. Our previous study had shown comparable normal forces

between the ulnar fingers for a handle mass of 0.535kg20. In another study on investigating the role of grasp force magnitude during multi-finger prehension22, by suspending an external load

of mass 0.160 kg eccentrically at various distances under a handle of mass 0.415 kg, the contribution of digit forces in terms of percentage of total normal force of the virtual finger was

examined. It was found that even for a small external torque of 0.14 Nm, during natural grasping, the percentage share of the little finger normal force (approx. 45%) was greater than the

ring finger normal force (approx. 33%). The total mass of the handle (0.450 kg) with the minimum external load (0.150 kg) used in our current study was approximately close to the total mass

of the grip device in the afore-mentioned multi-finger prehension study22 in which MAH was supported. Hence, we hypothesized that the mechanical advantage hypothesis would be supported for

all our experimental conditions (0.150, 0.250, 0.350, and 0.450 kg) of external load starting with a minimal mass of 0.150 kg (Hypothesis H1). METHODS AND MATERIALS PARTICIPANTS Twelve

young, healthy right-handed male volunteers participated in this study. The mean and standard deviation of the participant’s age, height, weight, hand length, and width were measured as

follows: Age: 26.75 ± 3.9 years, Height: 172.02 ± 5.7 cm, Weight: 75.21 ± 17.7 kg, Hand-length: 18.93 ± 1.1 cm, and Hand-width: 8.92 ± 0.7 cm). Only participants with no history of

neurological diseases and musculoskeletal injuries were chosen to participate in this experiment. ETHICS APPROVAL The Institutional Ethics committee of the Indian Institute of Technology

Madras approved the experimental procedures (Approval Number: IEC/2021-01/SKM/02/05). All the participants gave written informed consent according to the procedure approved by the

institutional ethics committee of IIT Madras before the beginning of the experiment. The experimental sessions were conducted by strictly adhering to the procedures approved by the

Institutional Ethics Committee of the Indian Institute of Technology Madras. EXPERIMENTAL SETUP A five-finger prehensile handle was designed and custom-built for the experiment, as shown in

Fig. 1 (refer Supplementary Video S6). The handle consists of a vertical railing of length 13.6 cm fitted on the thumb side to mount the slider platform, thus allowing its vertical

translation along the railing. The handle was suspended from wooden support using a nylon rope housed within a hollow PVC pipe to restrict any undesirable lateral movement while it was

suspended. The present study involves a prismatic precision grip of the handle of mass 0.450 kg. The mass of the slider platform was 0.100 kg. Thus, restricting the thumb tangential force to

approximately 1 N. Five six-axis force/torque sensors (Nano 17, Force resolution: Tangential: 0.0125 N, Normal: 0.0125 N, ATI Industrial Automation, NC, USA) was mounted on the handle to

measure the forces and the moments exerted by the individual fingers and thumb. For the thumb alone, the force sensor was placed on the slider platform, which enabled the smooth translation

of the platform over the railing fitted on the handle's thumb side. A laser displacement sensor (resolution, 5 μm; OADM 12U6460, Baumer, India) was mounted on a square flat piece made

of acrylic, and the assembly was fitted on top of the handle towards the thumb side. The displacement sensor provided the displacement data of the thumb platform in the vertical direction

while it translated along the vertical railing. On top of the handle, another acrylic block was placed in the anterior–posterior direction, which held an intelligent 9-axis absolute

orientation sensor (Resolution: 16bits, Range: 2000°/s, Model: BNO055, BOSCH, Germany). This IMU (Inertial Measurement Unit) sensor provided the orientation data of the handle after

appropriate pre-processing of the raw data. A spirit level was also mounted on the acrylic block towards the participant’s side of the handle to aid the participant in ensuring the handle’s

vertical orientation while it was being held. Two horizontal lines were drawn on the participant’s side of the handle, one at the center of the thumb platform and another midway between

middle and ring fingers on the handle frame. The participants were asked to hold the handle in a way such that the two lines were aligned. Thirty analog signals from the force/torque sensors

(5 sensors × 6 components) and single-channel analog laser displacement data were digitized using NI USB 6225 and 6002 at 16-bit resolution (National Instruments, Austin, TX, USA). This

data was synchronized with four channels of processed, digital data from the IMU sensor. Sampling rates of all data were set to 100 Hz. EXPERIMENTAL PROCEDURE Participants were asked to wash

and clean their hands with soap, towel-dry and then sit comfortably on a wooden chair with their forearm resting on the table. The right upper arm was abducted at approximately 45° in the

frontal plane, flexed 45° in the sagittal plane, and elbow flexed at approximately 90°. The natural grasping position can be achieved by supinating the forearm at 90°. The movements of the

forearm and wrist were constrained by fastening with a Velcro strap to the tabletop. The experiment involved four conditions. For these conditions, external loads of mass 0.150, 0.250,

0.350, and 0.450 kg were added at the bottom of the handle, i.e., exactly under the center of mass of the handle. A computer monitor displayed a solid horizontal target line with two dashed

lines at 0.2 cm above and below the target line. These dashed lines represented an acceptable error margin. The target line shown on the monitor corresponded to the ‘HOME position’ of the

thumb. The trial began only after the participant could hold the thumb platform steadily by aligning the horizontal line on the thumb platform to the line drawn midway between the middle and

ring finger. Thumb displacement data measured using a laser displacement sensor was shown as feedback on the participant’s screen. Once the trial started, the participants were required to

keep the slider platform in the same position (HOME), by aligning the horizontal line on the platform to the line drawn between the middle and the ring fingers. Precise alignment of the two

lines during the task essentially meant that the feedback line traced the actual target line. Acceptable performance or task success during the trial was defined to be within an error margin

of ± 0.2 cm as mentioned above. Throughout the trial, the handle had to be maintained in static equilibrium in the frontal plane for all the external loads. This was ensured by having the

bubble of the spirit level at the center throughout the trial. For each experimental condition, 25 trials were performed. Each trial lasted for six seconds. One minute of break was provided

between trials. After every twelve trials, ten minutes of break was provided to eliminate the effect of over exertion, if any. The experiment was held in two separate sessions. Each session

included two external load conditions with thirty minutes of break between conditions. The order of presentation of these two sessions was counterbalanced across all participants (see

Supplementary Table S7). Six of the participants performed with the weight of 0.150 kg followed by 0.350 kg in their first session. The other six participants performed with the weight of

0.450 kg followed by 0.250 kg in their first session (refer Supplementary Note and Fig. S8). DATA ANALYSIS The data were analyzed offline using MATLAB (Version R2016b, MathWorks, USA).

Force/Torque data and laser displacement data of thumb were lowpass filtered at 15 Hz using second-order, zero phase lag Butterworth filter. In each trial, the data between 2 and 5 s were

taken for analysis to avoid start and end effects. The normal and tangential force data collected from the individual fingertips and the thumb were averaged over the time samples, trials,

and participants for each condition separately, and the standard errors of the mean were computed. STATISTICS All Statistical analyses were performed using R. Two-way repeated-measures ANOVA

was performed on the average normal force with the two factors being _loads_ (4 levels: 0.150, 0.250, 0.350, 0.450 kg) and _fingers_ (4 levels: index, middle, ring, little). Since the thumb

normal force is dependent on the normal forces of the index, middle, ring, and little fingers, a separate one-way repeated measures ANOVA was performed on the thumb normal force with the

factor as _loads_ (4 levels: 0.150, 0.250, 0.350, 0.450 kg). Another two-way repeated-measures ANOVA was performed on the average tangential force with the factors being _loads_ (4 levels:

0.150, 0.250, 0.350, 0.450 kg) and _fingers_ (5 levels: index, middle, ring, little, thumb). Sphericity test was done on the data, and the number of degrees of freedom was adjusted by

Huynh–Feldt (H–F) criterion wherever required. Pairwise post hoc tukey tests were performed to examine the significance within factors. Further, we performed equivalence tests for all the

non-different pairs. The statistical equivalence was tested using the two one-sided t-tests (TOST) approach23 for a desired statistical power of 95%. The smallest effect size of interest

(SESOI) was chosen as the equivalence bounds. RESULTS TASK PERFORMANCE All the participants were able to trace the horizontal target line shown on the monitor within the error margin during

all four loading conditions (0.150, 0.250, 0.350, and 0.450 kg) as shown in Supplementary Fig. S1. Root mean squared error (RMSE) on the thumb displacement data was computed for the four

different loads and is shown in Table 1. Throughout the trial, the participants attempted to maintain the handle in static equilibrium during all four loading conditions by positioning the

bubble at the center of the bull’s eye. Therefore, the average net tilt angles for the different loading conditions were found to be less than one degree, as shown in Table 1. Thus, the

participants could trace the target line with minimal vertical displacement and minimal tilt during all trials in all loading conditions. NORMAL FORCES OF THE INDIVIDUAL FINGERS AND THUMB

DURING DIFFERENT LOADS The normal forces of the ring and little fingers were found to be statistically comparable with the addition of external loads of 0.150, 0.250, and 0.350 kg. However,

when an external load of 0.450 kg was added, the little finger normal force was found to be statistically (_p_ < 0.0001) greater than the ring finger normal force and thus supporting MAH.

We observed a main effect of the factor _loads_ (F(2.73, 30.03) = 8.571; _p_ < 0.001, η2p = 0.43) when a two-way repeated-measures ANOVA was performed on the absolute normal force with

the factors as _loads_ and _fingers_. It was found that the normal forces of the individual fingers (excluding the thumb) under the loading condition of 0.450 kg were statistically (_p_ <

 0.001) greater than the normal forces produced under loading conditions of 0.150 and 0.250 kg. Further, the normal forces produced with a load of 0.350 kg were statistically (_p_ < 0.05)

greater than the normal force produced with a load of 0.150 kg. In addition to this, there was a significant effect of the _fingers_ (F(3, 33) = 181.921; _p_ < 0.001, η2p = 0.94)

corresponding to a statistically (_p_ < 0.001) higher normal force by the little finger than the index, middle and ring fingers on loading (refer Fig. 2). Also, the normal force of the

ring finger was statistically greater than the index and middle fingers. Meanwhile, we also found that the ring and little finger normal forces were non-different when external loads of

masses 0.150 kg (t(11) = − 1.129, _p_ = 0.283, dz = 0.32), 0.250 kg (t(11) = − 0.978, _p_ = 0.349, dz = 0.28) and 0.350 kg (t(11) = − 1.454, p = 0.174, dz = 0.41) were employed. Therefore,

by using TOST procedure on the dependent pairs (0.150 kg: Ring: Mean = 4.55 N, SD = 0.55; Little: Mean = 4.75 N, SD = 0.45; 0.250 kg: Ring: Mean = 4.84 N, SD = 0.90; Little: Mean = 5.07 N,

SD = 0.50; 0.350 kg: Ring: Mean = 5.29 N, SD = 0.78; Little: Mean = 5.70 N, SD = 0.58), it was confirmed that the ring and little finger normal forces were statistically equivalent (0.150 

kg: t(11) = 2.473, _p_ = 0.0155; 0.250 kg: t(11) = 2.625, _p_ = 0.0118; 0.350 kg: t(11) = 2.148, _p_ = 0.0274) with the observed effect size that falls within the equivalence bounds of ∆L = 

− 1.04 and ∆U = 1.04 under the loads of 0.150, 0.250 and 0.350 kg. The interaction _loads_ × _fingers_ was significant (F(3.96, 43.56) = 18.538; _p_ < 0.001, η2p = 0.62) reflecting the

fact that the ring and little finger normal forces of 0.450 kg (Ring: 5.03 N, Little: 6.94 N), 0.350 kg (Ring: 5.29 N, Little: 5.70 N), 0.250 kg (Ring: 4.84 N; Little: 5.07 N), were

statistically (_p_ < 0.001) greater than the index and middle finger normal forces (0.150 kg: Index: 1.79 N, Middle: 2.58 N; 0.250 kg: Index: 1.54 N, Middle: 2.46 N; 0.350 kg: Index: 1.55

 N, Middle: 2.81 N; 0.450 kg: Index: 1.68 N, Middle: 2.79 N) of all the loading conditions (refer Fig. 3). While, the pairwise post hoc tukey tests confirmed that the little finger normal

force (6.94 N) of 0.450 kg was statistically (_p_ < 0.001) greater than the ring and little finger normal forces (0.150 kg: Ring: 4.55 N, Little: 4.75 N; 0.250 kg: Ring: 4.84 N, Little:

5.07 N; 0.350 kg: Ring: 5.29 N, Little: 5.70 N (_p_ < 0.01)) of the remaining loads (see Fig. 3). Whereas a little finger (5.70 N) of 0.350 kg produced statistically (p < 0.01) greater

normal force than the ring finger (4.55 N) under 0.150 kg of load. One-way repeated-measures ANOVA was performed on the thumb normal force, which showed a significant effect of the factor

loads (F(2.69, 88.90) = 9.411; _p_ < 0.001, η2p = 0.46). Under the loading of 0.450 kg, the thumb normal force (16.50 N) was found to be statistically greater than under loadings of 0.150

 kg (13.73 N, _p_ < 0.01) and 0.250 kg (13.97 N, _p_ < 0.05) (see Supplementary Fig. S2). TANGENTIAL FORCES OF INDIVIDUAL FINGERS DURING DIFFERENT LOADS In the case of the tangential

forces, a two-way repeated-measures ANOVA with the factors as _loads_ (F(3, 33) = 390.575; _p_ < 0.001, η2p = 0.97) and _fingers_ (F(4, 44) = 44.205; _p_ < 0.001, η2p = 0.80) showed

significant effect of the factor _loads_ corresponding to a statistically greater tangential force with the use of 0.450 kg than with the use of 0.150 kg (_p_ < 0.001), 0.250 kg (_p_ <

 0.001) and 0.350 kg (_p_ < 0.05). In addition, a significant effect of the factor _fingers_ confirmed that the little finger tangential force was statistically (_p_ < 0.001) greater

than the index, middle, and ring finger tangential forces on loading. In addition to this, on performing the pairwise post hoc tukey test, it was confirmed that the little finger tangential

force (0.150 kg: 2.03 N, 0.350 kg: 2.80 N) was non-different from the ring finger tangential force during the employment of 0.150 kg (1.64 N) and 0.350 kg (2.26 N). TOST procedure performed

on these dependent pairs confirmed that the comparisons were not statistically equivalent. However, little finger tangential force (0.450 kg: 3.22 N; 0.250 kg: 2.54 N) was statistically

greater than the ring finger tangential force with the addition of load 0.450 kg (Ring: 2.52 N, _p_ < 0.01) and 0.250 kg (Ring: 1.92 N, _p_ < 0.05) (refer Fig. 4). Further, interaction

effect of _loads_ x _fingers_ was significant (F(12, 132) = 5.857; _p_ < 0.001, η2p = 0.34) reflecting the fact that the little finger tangential forces (3.22 N) due to the use of 0.450 

kg was statistically greater than the ring and little finger tangential forces (0.150 kg: Ring: 1.64 N, _p_ < 0.01, Little: 2.03 N, _p_ < 0.001; 0.250 kg: Ring:1.92 N, _p_ < 0.001,

Little: 2.54 N, _p_ < 0.05; 0.350 kg: Ring: 2.26 N, _p_ < 0.001) due to the other loads (refer Supplementary Fig. S3). DISCUSSION The main objective of the present study was to

investigate whether the applicability of MAH is dependent solely on task parameters like the total weight of the handle, moment arm of the suspended load, or is it affected by factors beyond

these physical parameters. We tested the manifestation of MAH in our paradigm by systematically increasing the weight of the handle by adding external loads at the bottom of the handle

below its center of mass. The weight of our current handle with the minimal loading condition exceeded the weight of the handle in our previous study20. So, we hypothesized that MAH would be

supported in all our loading conditions. Contrary to our expectation, we found that the ring and little finger normal forces were statistically comparable with the addition of 0.150, 0.250,

and 0.350 kg loads. However, we noticed that MAH was supported for the external load of 0.450 kg. We discuss the implications of these findings in the following paragraphs. Ulnar finger

normal forces were examined under four different external loading conditions i.e., 0.150, 0.250, 0.350 and 0.450 kg. In our previous study, with a similar unsteady thumb platform as used in

the current study, the ulnar fingers produced comparable normal forces for a handle mass of 0.535 kg20. With the minimal external load of 0.150 kg, the total mass of the handle would become

0.600 kg (above 0.535 kg that was used in our previous study). So, our expectation was that MAH would be supported for all the loading conditions. In contrast to our expectation, the little

finger produced statistically comparable normal forces to the ring finger for 0.150 kg load. With further increase in the external loadings with masses 0.250 and 0.350 kg, the ulnar fingers

continued exhibiting statistically comparable normal forces. However, this trend did not hold true when the external load was increased to 0.450 kg, wherein the little finger exerted a

statistically greater normal force than the ring finger. Unlike the other studies on grasping with eccentrically loaded manipulanda, the current study involved maintaining a constant minimal

tangential force by the thumb (approximately 1 N) at different loading conditions (see Supplementary Fig. S4). Therefore, with an increase in the total mass of the handle by adding an

external load of 0.450 kg (comparatively larger than the mass of other loads employed in the present study), the virtual finger had to share greater tangential force to maintain the vertical

equilibrium causing a greater pronation torque (counter-clockwise direction from the participants viewpoint). This, in turn, necessitated progressively greater compensatory supination

moments to maintain the rotational equilibrium. Since the design of the handle prevents the thumb from contributing further to the supination moment, the ulnar fingers are required to

compensate with their normal forces. In this regard, instead of exerting comparable normal forces, the little finger tends to produce greater normal force than the ring finger, thus

supporting MAH. What could be the reason for this behavior of ulnar fingers with the addition of the heaviest external load as compared to the other loads? The next natural question is

whether the applicability of mechanical advantage depends on employing heavy masses while grasping. If that had been true, then MAH would have been supported when a large external load of 2 

kg was suspended at a distance of 1.9 cm from the center of mass (COM) of the handle (for a torque magnitude of − 0.375Nm) in the grasping study investigating the contribution of peripheral

and central fingers17. However, they found that ulnar fingers normal forces were non-different for this large load. Eventually, with a systematic increase in the compensatory supination

torque magnitude (0.750, 1.125, and 1.50Nm), the little finger gradually started producing more normal force than the ring finger and validated the MAH. In another study investigating the

role of grasp force magnitude during multi-finger prehension22, when an external load of mass 0.160 kg (much lesser than 2 kg) was suspended from a handle of mass 0.415 kg eccentrically at a

distance of 8.9 cm from COM, MAH was supported. This result triggers another question as to whether the support for MAH depends on suspending the external load at large moment arms from COM

of the handle? From the results of the multi-finger prehension study22, it was apparent that the applicability of mechanical advantage depends on using higher moment arms for the external

load. Our current result forces us to re-evaluate this conclusion, as MAH was supported even when an external load of 0.450 kg was suspended directly below COM of the handle (having zero

moment arm). This suggests that apart from the mass of the external load and moment arm of the suspended load, a latent factor governs the applicability of mechanical advantage. In other

words, our data suggest that the applicability of the principle of mechanical advantage in biological systems depends not only on the mass or moment arm of the suspended load or both but

also on more individual-specific components such as the individual ability of managing a task. In the prehension study investigating the effect of grasp force magnitude22, the demanding

aspect of the task might have been using an unusually high moment arm, thus allowing MAH to manifest. In a recent study24 using a handle similar to the current study, the task was to trace

trapezoid and inverted trapezoid patterns by displacing the thumb platform 1.5 cm above and below the HOME position. The mechanical advantage hypothesis was supported during the inverted

trapezoid condition when the movable thumb platform was held steady while tracing the static portion 1.5 cm below the HOME (at the level below the center of the ring finger sensor). The

carpometacarpal joint (CMC) of the thumb has a restricted range of motion in the downward direction25 (flexion or radial adduction). Therefore, the task of maintaining the handle in static

equilibrium with a movable thumb platform at the level below the center of the ring finger sensor might have been quite difficult to perform. We suggest that this biomechanical constraint

which imparted difficulty in accomplishing the task may have caused the little finger to share greater normal force than the ring finger. Following a similar rationale, in the current study,

perhaps the task became fairly demanding, as the requirement was to produce compensatory supination torque with only the normal forces of the ulnar fingers. This was a direct effect of

restricting the thumb tangential force to a constant minimal magnitude and essentially rendering it much less consequential in the supination torque production. Simultaneously, this also

amplified the role of the ulnar fingers in the compensatory torque production. For the heaviest external load of 0.450 kg, the magnitude of fingertip forces required were much higher than

the magnitude of fingertip forces in the relatively easier loading conditions i.e., for the 0.150, 0.250, 0.350 kg loads. According to a study that investigated the use of mechanical

advantage in multi-finger torque production15, MAH is employed to reduce the total effort or force produced for the task without compromising to produce the required moment. Along similar

lines, we speculated that to avoid higher exertion (higher force levels) of the ulnar fingers by sharing comparable and greater forces (due to tangential force restriction in the thumb), the

participants used the mechanical advantage of the little finger to more efficiently manage the grasp after a threshold difficulty was reached. As per the instruction to participants in the

current study, the participants were allowed to continue performing the trials only when they did not feel over exertion or pain. Therefore, to successfully complete the task, without

indulging in straining the ring and little fingers, participants would have chosen to minimize the total force (or effort) in the ulnar fingers by employing the principle of mechanical

advantage. Also, from literature26, it was found that the exclusion of the little finger from the overall grip pattern decreased overall grip strength by 33%, and exclusion of the ring

finger from the overall grip pattern decreased overall grip strength by 21%. This shows that, among the ring and little fingers, little finger contribution is fairly higher than the ring

finger when there is an increase in overall grip force requirement. Thus, an addition of heavier external load, which in turn increases overall grip force requirement, might have caused the

little finger to contribute significantly greater than the ring finger. From an anatomical perspective, the little finger has an additional group of intrinsic muscles (hypothenar muscles)

compared to the ring finger, which could be a supporting factor to employ little finger than ring finger when the task becomes difficult or demanding. To further elucidate our result, it is

important to emphasize that in the previous studies on object manipulation that introduced external torques to the handle, there was no restriction in the distribution of tangential forces

among the fingers and the thumb while grasping. The tangential force of the thumb would have greatly contributed to the supination torque in addition to the normal forces of the ulnar

fingers. This was evident from the previous study17, where the thumb tangential force increased during the supination efforts. Hence, the participants might have been able to share

comparable normal forces by the ring and little fingers even with a larger load (2 kg) and with a greater torque magnitude of 0.375 Nm than in the current study. In contrast, in our current

study, the tangential force of the thumb was restricted to approximately 1 N by placing the thumb on a freely movable platform of mass 0.100 kg for all the loading conditions. This

essentially creates a situation wherein the ulnar fingers are forced to contribute greatly to the compensatory supination torque. We posit that such a constraint in the tangential force

contribution of the thumb is most exemplified under 0.450 kg external load. Note that this load is much less than the 2 kg load where MAH was not supported. We strongly believe that

individual-specific components such as the individual ability of managing a task that is difficult to accomplish might have encouraged the use of the mechanical advantage of the little

finger. The difficulty faced by the performer is not dictated merely by the external loads and torques but also due to the biomechanical constraint as in the previous study24, or it could be

due to the individual’s ability of managing a task. In the present study, the participants could complete the task under loads of 0.150, 0.250, and 0.350 kg (resulting in the supination

torques of 0.22, 0.23, and 0.25 Nm, respectively), which might not have been difficult enough than with a load of mass 0.450 kg (refer Fig. 5 and Supplementary Fig. S5). As under a load of

mass 0.450 kg, the task of maintaining the static equilibrium of the handle by producing greater and comparable forces by the ulnar fingers might have been difficult. Therefore, for

successful completion of the task, little finger having both mechanical and anatomical advantage would have produced greater force than ring finger. Whereas, due to the task simplicity,

comparable normal forces would be produced by the ulnar fingers, with the addition of 0.150, 0.250, and 0.350 kg loads. In a study on producing maximum voluntary contraction MVC27, when the

target finger is the little finger, the force produced by the little finger was found to be well above the adjacent ring finger force. Analogously, since our study involved very strong

voluntary grasping of the handle for the external loading condition of 0.450 kg, greater activation of the little finger motor units could have caused a greater force in the little finger

than the ring finger, thus enabling optimal distribution of forces within the ulnar fingers in line with the MAH. This is also supported by the study28 wherein they found that the magnitude

of force produced due to the little finger motor units under the ring finger was almost two-thirds of the force produced under little finger during voluntary grasping. Since we have not

measured the actual activation pattern of the individual motor units, further research is required to tease out the underlying neural mechanisms through which mechanical advantage is

manifested. Taken together, our results suggest that the applicability of the mechanical advantage hypothesis depends not only on the torque requirement or the total mass of the object but

also on the individual’s ability to manage the task. CONCLUDING COMMENTS The current study was performed to validate whether the mechanical advantage hypothesis is task-specific and

investigate the kind of tasks that lend support to the MAH. A five-finger prehensile handle with an unsteady thumb platform was utilized for analysing the applicability of MAH. The mass of

the handle was systematically increased by using additional external loads of mass 0.150, 0.250, 0.350, and 0.450 kg. Ulnar fingers exerted comparable normal forces with the external loads

of mass 0.150, 0.250, and 0.350 kg. However, the mechanical advantage hypothesis was supported with a load of 0.450 kg. With the addition of greater mass, under the constraint of using

minimal thumb tangential force, establishing static equilibrium by the ulnar fingers becomes progressively more challenging. Therefore, we conclude that MAH as a strategy utilised in human

grasping is not only employed when there is any change in the mass of the grasped handle or moment arm of the suspended load but also when a certain threshold difficulty is reached during

the task. DATA AVAILABILITY We plan to publish a data descriptor article along with this manuscript. Hence the data will be made available in due course of time. The data descriptor article

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Article  CAS  Google Scholar  Download references ACKNOWLEDGEMENTS We thank the Department of Science & Technology, Government of India, for supporting this work, vide Reference Nos

SR/CSRI/97/2014 & DST/CSRI/2017/87 under Cognitive Science Research Initiative (CSRI) (awarded to Varadhan SKM), American Express (funding awarded to DART lab, IIT Madras) and “Women

leading IIT Madras (WLI)” grant (awarded to Banuvathy Rajakumar). The funders had no role in study design, data collection, and analysis, decision to publish, or preparation of the

manuscript. AUTHOR INFORMATION AUTHORS AND AFFILIATIONS * Department of Applied Mechanics, Indian Institute of Technology Madras, Tamil Nadu, Chennai, 600036, India Banuvathy Rajakumar, 

Swarnab Dutta & S. K. M. Varadhan Authors * Banuvathy Rajakumar View author publications You can also search for this author inPubMed Google Scholar * Swarnab Dutta View author

publications You can also search for this author inPubMed Google Scholar * S. K. M. Varadhan View author publications You can also search for this author inPubMed Google Scholar

CONTRIBUTIONS Conceptualization—B.R., V.S.K.M.; Methodology—B.R., S.D., V.S.K.M.; Formal Analysis—B.R.; Writing Original Draft—B.R.; Writing, Review, and Editing –B.R., S.D., V.S.K.M.

CORRESPONDING AUTHOR Correspondence to S. K. M. Varadhan. ETHICS DECLARATIONS COMPETING INTERESTS The authors declare no competing interests. ADDITIONAL INFORMATION PUBLISHER'S NOTE

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ARTICLE Rajakumar, B., Dutta, S. & Varadhan, S.K.M. Support for mechanical advantage hypothesis of grasping cannot be explained only by task mechanics. _Sci Rep_ 12, 10242 (2022).

https://doi.org/10.1038/s41598-022-14014-2 Download citation * Received: 07 November 2021 * Accepted: 31 May 2022 * Published: 17 June 2022 * DOI: https://doi.org/10.1038/s41598-022-14014-2

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