- Email: [email protected]
Grip force when grasping moving cylinders
ARTICLE IN PRESS
International Journal of Industrial Ergonomics 34 (2004) 69–76
Grip force when grasping moving cylinders A. Dubrowskia,*, H. Carnahanb a
Department of Surgery, University of Toronto, Surgical Skills Centre at Mount Sinai Hospital, 600 University Ave., Level 2- Room 250, Toronto, Ont., Canada M5G 1X5 b Department of Kinesiology, University of Waterloo, Waterloo, Ont., Canada N2L 3G1 Received 19 August 2003; received in revised form 6 February 2004
Abstract The purpose of this study was to examine the forces at the fingers that are produced when intercepting moving cylinders (in a simulated assembly line). The contributions of several characteristics of the moving cylinder on the grip and load forces produced at the fingers during capturing and lifting were studied. Specifically, the contributions of cylinder mass, velocity, momentum, and the transient torque values generated when the fingers contacted the cylinder were evaluated. Participants grasped heavy, medium and light cylinders that were instrumented with force/torque transducers that moved at slow, medium and fast velocities along a moving track. The masses and velocities were chosen such that several of the mass/velocity combinations shared the same momentum values. Results showed that both momentum (a product of both mass and velocity) and torque influenced grip force production. These results are discussed in terms of anticipatory versus on-line control of grasping, and worker safety. Relevance to industry The results of this study provide data about grip force production when intercepting and grasping moving cylinders that can be used for designing assembly line protocols for potentially reducing the increased force production that is associated with repetitive strain injury. r 2004 Elsevier B.V. All rights reserved. Keywords: Grasping; Force control; Assembly line performance
1. Introduction Understanding assembly line performance is important for both worker safety and enhancing productivity. While there is little research that has directly examined how people alter the movements of their hands in response to the motion of objects along an assembly line, it has been shown that the *Corresponding author. Fax: +1-416-340-3792. E-mail address: [email protected] (A. Dubrowski).
characteristics of target motion have a strong influence on the kinematics of the interception movement toward it. For example, as the velocity of the target increases, so does the velocity of the transport of the manual interception movement (Smeets and Brenner, 1995; van Donkelaar et al., 1992). However, Mason and Carnahan (1999) showed that when the target’s travel distance was manipulated so that targets were moving at the same velocity, but had different travel times, target velocity was not the critical variable in predicting interception velocity. Instead, they found that the
0169-8141/$ - see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.ergon.2004.03.001
ARTICLE IN PRESS 70
A. Dubrowski, H. Carnahan / International Journal of Industrial Ergonomics 34 (2004) 69–76
target’s travel time was the best predictor of interception velocity. The issue of cycle time on a paced assembly line has been recently examined, with models analyzing the probability of completing a job within a given cycle time on a mechanically paced assembly line (Johnson, 2002). While it is apparent from this example that speed of an assembly line is important, it is not clear how increasing speed, and mass of the objects being interacted with on the assembly line could affect the forces at the hands. The point has been made that disregarding the physical demands of minimizing cycle time may contribute to the development of workrelated musculoskeletal disorders in assembly line workers (Carnahan et al., 2001). Even nonforceful, repetitive tasks that require people to use the smaller muscles, contribute to the many muscle, tendon and nerve entrapment disorders that are reported (Stock, 1991; Shih et al., 2001). Also, workstation ergonomics in assembly lines has been shown to influence product quality (Lin et al., 2001). The purpose of this paper was to examine the forces at the fingers that are produced when intercepting moving cylinders (in a simulated assembly line) to understand some of the mechanisms involved in object capture. The results of this study, in addition to contributing to our theoretical understanding of target capture, will contribute to both worker safety and work output. It is not clear what patterns of forces produced by the fingers would be expected when capturing moving cylinders. One could assume that there is only one solution to the challenge of capturing a moving object. That is, when an individual grasps a moving object and decelerates it, grip force would be expected to be larger, the faster the object is moving. However, there are other strategies that could be adopted. For example, an individual could keep the amount of force generated constant as a function of increased target velocity, but instead vary the rate at which this force is applied. The closest examination of force control during target interception that exists in the literature involved participants holding a force transducer that was struck from the side by a pendulum released from various angles (Turrell et al., 1999). Turrell and colleagues found that grip
force increased as the impact force increased, in anticipation of the contact with the moving pendulum. These authors suggest that an important factor in regulating the grip forces on the transducer is the momentum associated with the transducer and the pendulum at impact. However, the actual values of momentum, or its role, were never directly examined. One purpose of the present study was to investigate the role of momentum during impact, between the fingers and a moving cylinder, on the production of grip and load force. When intercepting a moving cylinder, torques are created if the object is not grasped precisely in line with the center of mass. Depending on where the fingers contact the cylinder, the transient torque values can change, on a trial-to-trial basis. It has been demonstrated that to prevent the torques from rotating stationary objects that are held between the index finger and thumb, grip forces are increased (Kinoshita et al., 1997). It is hypothesized that in a dynamic situation, when grasping moving cylinders the control of torque that is created when the object is grasped outside the center of mass, may be even more important than in the static situation. Torque (t) is a product of force which is mass (m) times acceleration (a), and the length of the moment arm (d) (Eq. (1)). Linear momentum (p) is a product of object mass (m) and its velocity (V) (Eq. (2)). Thus, torque and linear momentum are mathematically related (Eq. (3)). t ¼ mad
ðNMÞ;
ð1Þ
p ¼ mv
ðkg m=sÞ;
ð2Þ
t ¼ pad=V :
ð3Þ
While one purpose of this study was to examine the contributions of torque to predicting grip force, torque was never directly manipulated. Thus far, we have identified transient torques, cylinder velocity and momentum as potential contributors to grip force production when contacting moving cylinders. However, momentum and velocity are also not independent since momentum is the product of cylinder velocity and mass. We know that when grasping stationary objects, mass has
ARTICLE IN PRESS A. Dubrowski, H. Carnahan / International Journal of Industrial Ergonomics 34 (2004) 69–76
been shown to influence grip and load force such that as object mass increases so does force production (Johansson and Westling, 1984). Thus, the effects of momentum on grip force could be due to the contributions of cylinder mass (independent of cylinder velocity). Using multiple regression modeling, one goal of this experiment was to partition out the variance in grip control contributed by the variables: torque, cylinder mass, velocity, and momentum.
2. Methods 2.1. Participants Eight healthy, self-reported right-handed human volunteers (3 females, 5 males; mean age 23.2 years, range 22–27 years) participated in the study. The participants had normal or corrected to normal vision. All gave informed consent before participating in this study. Approval from the
71
University of Waterloo Office of Research Ethics was obtained before testing began. 2.2. Apparatus The object to be grasped was a six-axis force-torque sensor (Nano F/T transducer; ATI Industrial Automation, Garner, NC) with two exchangeable polyethylene plastic cylindrical mass containers with flat grasping surfaces, mounted on each side of the sensor. The resulting cylinder was 5.5 cm wide and 3 cm in diameter. Refer to Shih et al. (2001) for a schematic of the cylinder. Changing the mass containers on each side of the sensor varied the total mass of the unit. The unit’s total weight was either 50, 100 or 200 g. Fig. 1 shows a schematic of the experimental setup. A step motor assembly (Applied Motion Products, motor model # 5023-124; driver model # PD5580) fitted with a chain socket system was used to move an aluminum platform, carrying the
Interception zone Hand Start 30 mm
Cylinder Start 360 mm
M
Fig. 1. This figure shows a schematic of the experimental setup. The motor (M) controlled the velocity of the cylinder. Note the orientation of the cylinder was perpendicular to the direction of movement. The insert at the top of the figure shows how the index finger and thumb grasped the cylinder.
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A. Dubrowski, H. Carnahan / International Journal of Industrial Ergonomics 34 (2004) 69–76
force transducer unit, down a 2.5 m track, that was positioned to the right of the participants midlines. The travel velocity of the platform could be set with a 0.012 m/s precision, and the travel distance with 0.1 mm precision. The cylinder moved at either 0.114, 0.227 or 0.457 m/s. The total travel distance of the platform was constant throughout all experimental sessions (360 mm), and was set such that the force transducer unit did not stop in the interception zone, but continued 30 mm past the center of the interception zone. This ensured that the cylinder was in motion when the participants grasped it. When the cylinder was lifted, the grip force was measured along the grip axis defined by the line joining the centers of the two grasp surfaces. The forces were collected at 400 Hz with a resolution of 0.025 N. The load force was defined as the vector sum of the two perpendicular forces acting in the orthogonal plane to the grip force axis. It should be noted that the forces were not measured at each digit/cylinder interface, but instead were measured from the center of the cylinder being lifted. The rates of both grip and load force were also calculated. Torque values were measured about the grip force axis at a resolution of 0.125 Nmm. The absolute values of the torques were taken since the directionality of the torques was not as critical as accurately representing the presence of any existing torque magnitudes. All data were filtered with a 14 Hz dual low pass Butterworth filter. 2.3. Task Each participant’s hand was positioned in line with the forearm, prone and with the index finger and thumb in a pinch position. The forearm position on the rest pad was determined such that for each participant the thumb and the index finger rested in the middle of the cylinder interception zone, and the elbow joint was at 90 . Participants were asked to grasp, lift and hold the moving cylinder as it passed through the interception zone. The cylinder was oriented perpendicular to the direction of movement (see Fig. 1). The cylinder was lifted 5 cm and maintained at this height for 2 s using a precision grip
Table 1 The cylinder masses and cylinder velocities are presented, along with the corresponding momentum conditions that resulted from these mass and velocity combinations Cylinder mass (g) 50 Cylinder velocity
100
200
0.114 m/s
5.71 gm/s
11.42 gm/s
22.83 gm/s
0.227 m/s 0.457 m/s
11.42 gm/s 22.83 gm/s
22.83 gm/s 45.74 gm/s
45.74 gm/s 91.45 gm/s
The matching momentum values are shown by similar superscript values.
between the index finger and the thumb, and repositioned back in the middle of the force transducer’s traveling platform. The lifting motion occurred at the wrist joint, with the forearm resting on a pad. Instantaneous linear momentum of a moving object is defined as a product of its mass and velocity. Thus, there were five possible linear momentum values (based on the three cylinder velocities and masses) for the cylinder as it passed through the interception zone and was grasped by the participant. As seen in Table 1, the momentum value of 11.4 gm/s was shared by the 50 g, 0.227 m/ s; and the 100 g, 0.114 m/s conditions. A momentum value of 22.8 gm/s was shared by the 50 g, 0.457 m/s; 100, 0.227 m/s; and the 200 g, 0.114 m/s conditions. Finally, the momentum value of 45.7 gm/s was shared by the 100 g, 0.457 m/s; and the 200 g, 0.227 m/s conditions. For the 50 g, 0.114 m/s condition the momentum value was 5.7 gm/s, and for the 200 g, 0.457 m/s condition the momentum value was 91.4 gm/s. This manipulation allowed a distinction between the relative contributions of cylinder mass, velocity and corresponding linear momentum to the generation of grip force. Ten trials of each of the cylinder velocities were performed consecutively for each of the blocks of cylinder mass. The presentation of these trial blocks was counterbalanced across participants. Prior to testing, each participant received a random presentation of two practice trials for each of the mass–velocity combinations.
ARTICLE IN PRESS A. Dubrowski, H. Carnahan / International Journal of Industrial Ergonomics 34 (2004) 69–76
2.4. Statistical analyses 2.4.1. Effects of cylinder velocity and cylinder mass To assess the contributions of cylinder velocity and mass on the peak torque, peak grip and load forces, and their associated rates, separate 3 (cylinder mass; 50, 100, 200 g) 3 (cylinder velocity; 0.114, 0.227, 0.457 m/s) repeated measures analyses of variance (ANOVAs) were run for each of these dependent measures. Effects significant at po0.05 were further analyzed using the Tukey HSD methods for post hoc comparison of means.
3. Results 3.1. Effects of cylinder velocity and cylinder mass 3.1.1. Grip force The peak grip force showed a main effect for cylinder mass, po0.01. Grip force increased as the mass of the cylinder increased. Statistically, less peak grip force was produced for the 50 g condition (3.3 N) in comparison to the 100 g (5.3 N) and 200 g (6.3 N) conditions. The 100 and 200 g conditions were not statistically different. However, the rate of grip force production showed main effects for both cylinder mass, po0.01 and cylinder velocity, po0.01. Grip force was produced with a lower rate when grasping the 50 g mass (34.9 N/s) in comparison to the 100 g (57.6 N/s) and 200 g (70.7 N/s) masses. There was no statistically significant difference between the 100 and 200 g masses. Also, the rate of grip force production was greater for the fast condition (71.7 N/s) in comparison to the medium (51.4 N/s) and slow (40.2 N/s) velocities, which did not differ statistically from each other. Means and standard errors for all dependent measures are seen in Fig. 2. 3.1.2. Load force The analysis of peak load force also showed a main effect for cylinder mass, p=0.01. Peak load force was greater when lifting the 200 g cylinder (2.1 N) in comparison to the 50 g cylinder (1.3 N). The peak load force generated when lifting the 100 g cylinder (1.6 N) did not differ statistically
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from either the 50 or 200 g conditions. The analysis of the rate of peak load force production showed main effects for both cylinder mass, p=0.01, and cylinder velocity, p=0.01. Load force rate was greater for the 200 g condition (27.6 N/s) in comparison to the 50 g condition (17.3 N/s), with the 100 g condition (23.2 N/s) not differing statistically from the other two conditions. Load force rate was also greater for the fast cylinder condition (27.7 N/s) in comparison to the slow condition (18.6 N/s), with the medium velocity condition (21.8 N/s) not differing statistically from the other two cylinder velocities. 3.1.3. Torque A main effect for mass was seen in the analysis of torque, po0.01. Peak torque was greater when lifting the 200 g cylinder (11.3 Nmm) in comparison to the 50 g cylinder (5.8 Nmm). The peak torque generated when lifting the 100 g cylinder (8.5 Nmm) did not differ statistically from either the 50 or 200 g conditions. Fig. 3 shows the strong influence of torque on grip force production. 3.2. Multiple regression To deal with the potential interrelationships between all the variables examined, a multiple regression analysis was run on the data that determined which of the predictor variables (cylinder velocity, cylinder mass, momentum) accounted for the most variance in grip force when the effect of torque on grip force was controlled for (Kinoshita et al., 1997). The correlation of grip force to load force was R2=0.9, thus the multiple regression analyses were run to account for variance in grip force only. The most parsimonious models, which could explain the observed variance, were selected based on step-wise selection (p=0.5 for entry and stay criteria) and by using the CP procedure (Daniel and Wood, 1980). As demonstrated in Table 2, the step-wise procedure selected model 1 as the model that accounted for the most variance in grip force. This model included transient torque values, intersubject differences and linear momentum of the cylinder as the variables that accounted for most
ARTICLE IN PRESS A. Dubrowski, H. Carnahan / International Journal of Industrial Ergonomics 34 (2004) 69–76
8 7 6 5 4 3 2 1
2.8 2.4 PLF (N)
PGF (N)
74
2.0 1.6 1.2 0.8
50
100
200
50
100
200
50
100
200
50 90
PLR (N/s)
GFR (N/s)
110 70 50 30 10
40 30 20 10
50
100
200
Torque (N.mm)
14 Object mass (g)
12 Speed (m/s)
10
0.114
8
50
100
200
5.7
11.4
22.8
6
0.227
11.35
22.7
45.4
4
0.457
22.85
45.7
91.4
50
100 200 Object mass (g)
Fig. 2. Means and standard errors for torque, peak grip and load force and the associated rates of force production, for the three mass and velocity conditions. Conditions with similar momentum values are indicated by solid lines. Note that there is a trend for conditions that share similar momentum values to also have similar patterns of force production.
of the variance in grip force generation. This model did not differ significantly from model 2, that contained mass and velocity in addition to torque and linear momentum, F(2,66)=0.31. As well, model 1 did not differ from model 3, that contained mass and velocity terms instead of the linear momentum term, F(1,67)=0.62. Thus since the model containing the transient torque, the subjects, and the linear momentum terms was the most parsimonious model (contains the least number of variables in order to explain the same amount of variance in the grip force,) it was chosen as the best predictor of grip force generation. This was confirmed by the CP procedure (C(p)=2.61).
4. Conclusions The purpose of this study was to examine the influence of the contributions of a moving cylinder’s velocity, mass, momentum, and torque, on the grip forces necessary for successful prevention. It was found that in a blocked presentation, as the cylinder mass increased, the grip and load forces involved in lifting it also increased (Johansson and Westling, 1984). While there was a trend for grasping forces to increase as cylinder velocity increased, this observation was not shown to be statistically significant. However, as the cylinder velocity increased so did the rate of force production when contacting and lifting the cylinder. The
ARTICLE IN PRESS A. Dubrowski, H. Carnahan / International Journal of Industrial Ergonomics 34 (2004) 69–76
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Fig. 3. Grip force and the transient torque values are plotted as a function of time for three representative trials for the 50 g, 0.457 m/s condition, and the 200 g, 0.114 m/s condition. The momentum value for both of these conditions was 22.8 gm/s. Grip force is shown by the solid black curve, the torque curves are dotted, and the dashed horizontal line is placed at the peak grip force of the plots for the 50 g, 0.457 m/s condition to serve as a reference. Panels A and B provide examples of trials where the torques for the two conditions were similar resulting in similar grip forces. In panel D, the trial (200 g, 0.114 m/s) with the high torque value has a corresponding higher grip force compared to panel C. In panel E, the opposite pattern was seen. In the 50 g, 0.457 m/s condition, a high transient torque value was observed and subsequently there was a higher grip force in comparison to panel F.
Table 2 Results of multiple regression analyses, where the predictor variables used were subject (S), cylinder mass (M) (g), cylinder velocity (V) (m/s), linear momentum (LM) (gm/s), and peak torque (Trq) (Nmm)
1 2 3
Model
R2
F (df)
GF=0.51+0.38S+0.02LM+0.36Trq+E GF=1.45+0.39S+0.01 M+0.002 V+0.002LM+0.35Trq+E GF=1.38+0.39S+0.01 M+0.002 V+0.35Trq+E
0.42 0.43 0.43
(3, 68)=16.90 (5, 66)=10.06 (4, 67)=12.76
observation that the actual generation of forces is influenced differentially by cylinder motion in comparison to the timing of force production, is similar to the observation by Mason and Carnahan (1999) that finger aperture size and timing are affected differentially when grasping moving cylinders. There may be independent mechanisms for grasp control that are responsible for the
timing versus the magnitude of associated muscular impulses. The results showed that as cylinder mass increased, grip force also increased. While there was a trend for cylinder velocity to show influence on grip force, there was no statistically significant effect. However, the multiple regression analysis chose the model that included the momentum of
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the cylinder a more parsimonious predictor of grip force than a model that included mass instead of momentum. Thus, while the effects of velocity were not statistically significant in the ANOVA, velocity did contribute in some form to grip force, as evidenced by the significant contributions of momentum (which is a product of cylinder velocity and mass). These data support the proposal made by Turrell et al. (1999) that momentum is an important variable that is represented in anticipatory models of force control (Johansson and Cole, 1994; Wolpert, 1997). The results of this study showed that the momentum of a moving target will influence the forces generated at the fingers during grasping. Thus, there is a larger potential for low-impact stress related injuries with repeated exposure to manual contact with faster/heavier moving objects. Thus, while increasing assembly line speed might speed up overall production, it could lead to increased worker injury. To help offset this potential for injury, increased assembly line speed could be offset with objects of smaller masses being manipulated.
Acknowledgements This research was supported by the Natural Sciences and Engineering Research Council of Canada.
References Carnahan, B.J., Norman, B.A., Redfern, M.S., 2001. Incorporating physical demand criteria into assembly line balancing. IEE Transactions 33, 875–887.
Daniel, C., Wood, F.S., 1980. Fitting Equations to Data, 2nd Edition. Wiley, New York. Johnson, D.J., 2002. A spreadsheet method for calculating work completion time probability distributions of paced or linked assembly lines. International Journal of Production Research 40, 1131–1153. Johansson, R.S., Cole, K.J., 1994. Grasp stability during manipulative actions. Canadian Journal of Physiology and Pharmacology 72, 511–524. Johansson, R.S., Westling, G., 1984. Roles of glaborous skin receptors and sensorimotor memory in automatic control of precision grip when lifting rougher or more slippery objects. Experimental Brain Research 56, 550–564. Kinoshita, H., Kawai, S., Ikuta, K., Teraoka, T., 1997. Individual finger forces acting on a grasped object during shaking actions. Ergonomics 243–256. Kinoshita, H., Backstrom, L., Flanagan, J.R., Johansson, R.S., 1997. Planar torque effects on grip force during precision grip. Journal of Neurophysiology 78, 1619–1630. Lin, L., Drury, C.G., Kim, S.W., 2001. Ergonomics and quality in paced assembly lines. Human Factors and Ergonomics in Manufacturing 11, 377–382. Mason, A.H., Carnahan, H., 1999. Target viewing time and velocity effects on prevention. Experimental Brain Research 127, 83–94. Shih, R.H., Vasarahelyi, E.M., Dubrowski, A., Carnahan, H., 2001. The effects of latex gloves on grasping kinetics. International Journal of Industrial Ergonomics 28, 265–273. Smeets, B.J., Brenner, E., 1995. Perception and action are based on the same visual information: distinction between position and velocity. Journal of Experimental Psychology: Human Perception and Performance 21, 19–31. Stock, S.R., 1991. Workplace ergonomic factors and the development of musculoskeletal disorders of the neck and upper limbs: a meta analysis. American Journal of Industrial Medicine 19, 87–107. Turrell, T.N., Li, F.-X., Wing, A.M., 1999. Grip force dynamics in the approach to a collision. Experimental Brain Research 128, 86–91. van Donkelaar, P., Lee, R.G., Gellman, R.S., 1992. Control strategies in directing the hand to moving targets. Experimental Brain Research 91, 151–161. Wolpert, D.M., 1997. Computational approaches to motor control. Trends in Cognitive Science 1, 209–216.
International Journal of Industrial Ergonomics 34 (2004) 69–76
Grip force when grasping moving cylinders A. Dubrowskia,*, H. Carnahanb a
Department of Surgery, University of Toronto, Surgical Skills Centre at Mount Sinai Hospital, 600 University Ave., Level 2- Room 250, Toronto, Ont., Canada M5G 1X5 b Department of Kinesiology, University of Waterloo, Waterloo, Ont., Canada N2L 3G1 Received 19 August 2003; received in revised form 6 February 2004
Abstract The purpose of this study was to examine the forces at the fingers that are produced when intercepting moving cylinders (in a simulated assembly line). The contributions of several characteristics of the moving cylinder on the grip and load forces produced at the fingers during capturing and lifting were studied. Specifically, the contributions of cylinder mass, velocity, momentum, and the transient torque values generated when the fingers contacted the cylinder were evaluated. Participants grasped heavy, medium and light cylinders that were instrumented with force/torque transducers that moved at slow, medium and fast velocities along a moving track. The masses and velocities were chosen such that several of the mass/velocity combinations shared the same momentum values. Results showed that both momentum (a product of both mass and velocity) and torque influenced grip force production. These results are discussed in terms of anticipatory versus on-line control of grasping, and worker safety. Relevance to industry The results of this study provide data about grip force production when intercepting and grasping moving cylinders that can be used for designing assembly line protocols for potentially reducing the increased force production that is associated with repetitive strain injury. r 2004 Elsevier B.V. All rights reserved. Keywords: Grasping; Force control; Assembly line performance
1. Introduction Understanding assembly line performance is important for both worker safety and enhancing productivity. While there is little research that has directly examined how people alter the movements of their hands in response to the motion of objects along an assembly line, it has been shown that the *Corresponding author. Fax: +1-416-340-3792. E-mail address: [email protected] (A. Dubrowski).
characteristics of target motion have a strong influence on the kinematics of the interception movement toward it. For example, as the velocity of the target increases, so does the velocity of the transport of the manual interception movement (Smeets and Brenner, 1995; van Donkelaar et al., 1992). However, Mason and Carnahan (1999) showed that when the target’s travel distance was manipulated so that targets were moving at the same velocity, but had different travel times, target velocity was not the critical variable in predicting interception velocity. Instead, they found that the
0169-8141/$ - see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.ergon.2004.03.001
ARTICLE IN PRESS 70
A. Dubrowski, H. Carnahan / International Journal of Industrial Ergonomics 34 (2004) 69–76
target’s travel time was the best predictor of interception velocity. The issue of cycle time on a paced assembly line has been recently examined, with models analyzing the probability of completing a job within a given cycle time on a mechanically paced assembly line (Johnson, 2002). While it is apparent from this example that speed of an assembly line is important, it is not clear how increasing speed, and mass of the objects being interacted with on the assembly line could affect the forces at the hands. The point has been made that disregarding the physical demands of minimizing cycle time may contribute to the development of workrelated musculoskeletal disorders in assembly line workers (Carnahan et al., 2001). Even nonforceful, repetitive tasks that require people to use the smaller muscles, contribute to the many muscle, tendon and nerve entrapment disorders that are reported (Stock, 1991; Shih et al., 2001). Also, workstation ergonomics in assembly lines has been shown to influence product quality (Lin et al., 2001). The purpose of this paper was to examine the forces at the fingers that are produced when intercepting moving cylinders (in a simulated assembly line) to understand some of the mechanisms involved in object capture. The results of this study, in addition to contributing to our theoretical understanding of target capture, will contribute to both worker safety and work output. It is not clear what patterns of forces produced by the fingers would be expected when capturing moving cylinders. One could assume that there is only one solution to the challenge of capturing a moving object. That is, when an individual grasps a moving object and decelerates it, grip force would be expected to be larger, the faster the object is moving. However, there are other strategies that could be adopted. For example, an individual could keep the amount of force generated constant as a function of increased target velocity, but instead vary the rate at which this force is applied. The closest examination of force control during target interception that exists in the literature involved participants holding a force transducer that was struck from the side by a pendulum released from various angles (Turrell et al., 1999). Turrell and colleagues found that grip
force increased as the impact force increased, in anticipation of the contact with the moving pendulum. These authors suggest that an important factor in regulating the grip forces on the transducer is the momentum associated with the transducer and the pendulum at impact. However, the actual values of momentum, or its role, were never directly examined. One purpose of the present study was to investigate the role of momentum during impact, between the fingers and a moving cylinder, on the production of grip and load force. When intercepting a moving cylinder, torques are created if the object is not grasped precisely in line with the center of mass. Depending on where the fingers contact the cylinder, the transient torque values can change, on a trial-to-trial basis. It has been demonstrated that to prevent the torques from rotating stationary objects that are held between the index finger and thumb, grip forces are increased (Kinoshita et al., 1997). It is hypothesized that in a dynamic situation, when grasping moving cylinders the control of torque that is created when the object is grasped outside the center of mass, may be even more important than in the static situation. Torque (t) is a product of force which is mass (m) times acceleration (a), and the length of the moment arm (d) (Eq. (1)). Linear momentum (p) is a product of object mass (m) and its velocity (V) (Eq. (2)). Thus, torque and linear momentum are mathematically related (Eq. (3)). t ¼ mad
ðNMÞ;
ð1Þ
p ¼ mv
ðkg m=sÞ;
ð2Þ
t ¼ pad=V :
ð3Þ
While one purpose of this study was to examine the contributions of torque to predicting grip force, torque was never directly manipulated. Thus far, we have identified transient torques, cylinder velocity and momentum as potential contributors to grip force production when contacting moving cylinders. However, momentum and velocity are also not independent since momentum is the product of cylinder velocity and mass. We know that when grasping stationary objects, mass has
ARTICLE IN PRESS A. Dubrowski, H. Carnahan / International Journal of Industrial Ergonomics 34 (2004) 69–76
been shown to influence grip and load force such that as object mass increases so does force production (Johansson and Westling, 1984). Thus, the effects of momentum on grip force could be due to the contributions of cylinder mass (independent of cylinder velocity). Using multiple regression modeling, one goal of this experiment was to partition out the variance in grip control contributed by the variables: torque, cylinder mass, velocity, and momentum.
2. Methods 2.1. Participants Eight healthy, self-reported right-handed human volunteers (3 females, 5 males; mean age 23.2 years, range 22–27 years) participated in the study. The participants had normal or corrected to normal vision. All gave informed consent before participating in this study. Approval from the
71
University of Waterloo Office of Research Ethics was obtained before testing began. 2.2. Apparatus The object to be grasped was a six-axis force-torque sensor (Nano F/T transducer; ATI Industrial Automation, Garner, NC) with two exchangeable polyethylene plastic cylindrical mass containers with flat grasping surfaces, mounted on each side of the sensor. The resulting cylinder was 5.5 cm wide and 3 cm in diameter. Refer to Shih et al. (2001) for a schematic of the cylinder. Changing the mass containers on each side of the sensor varied the total mass of the unit. The unit’s total weight was either 50, 100 or 200 g. Fig. 1 shows a schematic of the experimental setup. A step motor assembly (Applied Motion Products, motor model # 5023-124; driver model # PD5580) fitted with a chain socket system was used to move an aluminum platform, carrying the
Interception zone Hand Start 30 mm
Cylinder Start 360 mm
M
Fig. 1. This figure shows a schematic of the experimental setup. The motor (M) controlled the velocity of the cylinder. Note the orientation of the cylinder was perpendicular to the direction of movement. The insert at the top of the figure shows how the index finger and thumb grasped the cylinder.
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force transducer unit, down a 2.5 m track, that was positioned to the right of the participants midlines. The travel velocity of the platform could be set with a 0.012 m/s precision, and the travel distance with 0.1 mm precision. The cylinder moved at either 0.114, 0.227 or 0.457 m/s. The total travel distance of the platform was constant throughout all experimental sessions (360 mm), and was set such that the force transducer unit did not stop in the interception zone, but continued 30 mm past the center of the interception zone. This ensured that the cylinder was in motion when the participants grasped it. When the cylinder was lifted, the grip force was measured along the grip axis defined by the line joining the centers of the two grasp surfaces. The forces were collected at 400 Hz with a resolution of 0.025 N. The load force was defined as the vector sum of the two perpendicular forces acting in the orthogonal plane to the grip force axis. It should be noted that the forces were not measured at each digit/cylinder interface, but instead were measured from the center of the cylinder being lifted. The rates of both grip and load force were also calculated. Torque values were measured about the grip force axis at a resolution of 0.125 Nmm. The absolute values of the torques were taken since the directionality of the torques was not as critical as accurately representing the presence of any existing torque magnitudes. All data were filtered with a 14 Hz dual low pass Butterworth filter. 2.3. Task Each participant’s hand was positioned in line with the forearm, prone and with the index finger and thumb in a pinch position. The forearm position on the rest pad was determined such that for each participant the thumb and the index finger rested in the middle of the cylinder interception zone, and the elbow joint was at 90 . Participants were asked to grasp, lift and hold the moving cylinder as it passed through the interception zone. The cylinder was oriented perpendicular to the direction of movement (see Fig. 1). The cylinder was lifted 5 cm and maintained at this height for 2 s using a precision grip
Table 1 The cylinder masses and cylinder velocities are presented, along with the corresponding momentum conditions that resulted from these mass and velocity combinations Cylinder mass (g) 50 Cylinder velocity
100
200
0.114 m/s
5.71 gm/s
11.42 gm/s
22.83 gm/s
0.227 m/s 0.457 m/s
11.42 gm/s 22.83 gm/s
22.83 gm/s 45.74 gm/s
45.74 gm/s 91.45 gm/s
The matching momentum values are shown by similar superscript values.
between the index finger and the thumb, and repositioned back in the middle of the force transducer’s traveling platform. The lifting motion occurred at the wrist joint, with the forearm resting on a pad. Instantaneous linear momentum of a moving object is defined as a product of its mass and velocity. Thus, there were five possible linear momentum values (based on the three cylinder velocities and masses) for the cylinder as it passed through the interception zone and was grasped by the participant. As seen in Table 1, the momentum value of 11.4 gm/s was shared by the 50 g, 0.227 m/ s; and the 100 g, 0.114 m/s conditions. A momentum value of 22.8 gm/s was shared by the 50 g, 0.457 m/s; 100, 0.227 m/s; and the 200 g, 0.114 m/s conditions. Finally, the momentum value of 45.7 gm/s was shared by the 100 g, 0.457 m/s; and the 200 g, 0.227 m/s conditions. For the 50 g, 0.114 m/s condition the momentum value was 5.7 gm/s, and for the 200 g, 0.457 m/s condition the momentum value was 91.4 gm/s. This manipulation allowed a distinction between the relative contributions of cylinder mass, velocity and corresponding linear momentum to the generation of grip force. Ten trials of each of the cylinder velocities were performed consecutively for each of the blocks of cylinder mass. The presentation of these trial blocks was counterbalanced across participants. Prior to testing, each participant received a random presentation of two practice trials for each of the mass–velocity combinations.
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2.4. Statistical analyses 2.4.1. Effects of cylinder velocity and cylinder mass To assess the contributions of cylinder velocity and mass on the peak torque, peak grip and load forces, and their associated rates, separate 3 (cylinder mass; 50, 100, 200 g) 3 (cylinder velocity; 0.114, 0.227, 0.457 m/s) repeated measures analyses of variance (ANOVAs) were run for each of these dependent measures. Effects significant at po0.05 were further analyzed using the Tukey HSD methods for post hoc comparison of means.
3. Results 3.1. Effects of cylinder velocity and cylinder mass 3.1.1. Grip force The peak grip force showed a main effect for cylinder mass, po0.01. Grip force increased as the mass of the cylinder increased. Statistically, less peak grip force was produced for the 50 g condition (3.3 N) in comparison to the 100 g (5.3 N) and 200 g (6.3 N) conditions. The 100 and 200 g conditions were not statistically different. However, the rate of grip force production showed main effects for both cylinder mass, po0.01 and cylinder velocity, po0.01. Grip force was produced with a lower rate when grasping the 50 g mass (34.9 N/s) in comparison to the 100 g (57.6 N/s) and 200 g (70.7 N/s) masses. There was no statistically significant difference between the 100 and 200 g masses. Also, the rate of grip force production was greater for the fast condition (71.7 N/s) in comparison to the medium (51.4 N/s) and slow (40.2 N/s) velocities, which did not differ statistically from each other. Means and standard errors for all dependent measures are seen in Fig. 2. 3.1.2. Load force The analysis of peak load force also showed a main effect for cylinder mass, p=0.01. Peak load force was greater when lifting the 200 g cylinder (2.1 N) in comparison to the 50 g cylinder (1.3 N). The peak load force generated when lifting the 100 g cylinder (1.6 N) did not differ statistically
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from either the 50 or 200 g conditions. The analysis of the rate of peak load force production showed main effects for both cylinder mass, p=0.01, and cylinder velocity, p=0.01. Load force rate was greater for the 200 g condition (27.6 N/s) in comparison to the 50 g condition (17.3 N/s), with the 100 g condition (23.2 N/s) not differing statistically from the other two conditions. Load force rate was also greater for the fast cylinder condition (27.7 N/s) in comparison to the slow condition (18.6 N/s), with the medium velocity condition (21.8 N/s) not differing statistically from the other two cylinder velocities. 3.1.3. Torque A main effect for mass was seen in the analysis of torque, po0.01. Peak torque was greater when lifting the 200 g cylinder (11.3 Nmm) in comparison to the 50 g cylinder (5.8 Nmm). The peak torque generated when lifting the 100 g cylinder (8.5 Nmm) did not differ statistically from either the 50 or 200 g conditions. Fig. 3 shows the strong influence of torque on grip force production. 3.2. Multiple regression To deal with the potential interrelationships between all the variables examined, a multiple regression analysis was run on the data that determined which of the predictor variables (cylinder velocity, cylinder mass, momentum) accounted for the most variance in grip force when the effect of torque on grip force was controlled for (Kinoshita et al., 1997). The correlation of grip force to load force was R2=0.9, thus the multiple regression analyses were run to account for variance in grip force only. The most parsimonious models, which could explain the observed variance, were selected based on step-wise selection (p=0.5 for entry and stay criteria) and by using the CP procedure (Daniel and Wood, 1980). As demonstrated in Table 2, the step-wise procedure selected model 1 as the model that accounted for the most variance in grip force. This model included transient torque values, intersubject differences and linear momentum of the cylinder as the variables that accounted for most
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8 7 6 5 4 3 2 1
2.8 2.4 PLF (N)
PGF (N)
74
2.0 1.6 1.2 0.8
50
100
200
50
100
200
50
100
200
50 90
PLR (N/s)
GFR (N/s)
110 70 50 30 10
40 30 20 10
50
100
200
Torque (N.mm)
14 Object mass (g)
12 Speed (m/s)
10
0.114
8
50
100
200
5.7
11.4
22.8
6
0.227
11.35
22.7
45.4
4
0.457
22.85
45.7
91.4
50
100 200 Object mass (g)
Fig. 2. Means and standard errors for torque, peak grip and load force and the associated rates of force production, for the three mass and velocity conditions. Conditions with similar momentum values are indicated by solid lines. Note that there is a trend for conditions that share similar momentum values to also have similar patterns of force production.
of the variance in grip force generation. This model did not differ significantly from model 2, that contained mass and velocity in addition to torque and linear momentum, F(2,66)=0.31. As well, model 1 did not differ from model 3, that contained mass and velocity terms instead of the linear momentum term, F(1,67)=0.62. Thus since the model containing the transient torque, the subjects, and the linear momentum terms was the most parsimonious model (contains the least number of variables in order to explain the same amount of variance in the grip force,) it was chosen as the best predictor of grip force generation. This was confirmed by the CP procedure (C(p)=2.61).
4. Conclusions The purpose of this study was to examine the influence of the contributions of a moving cylinder’s velocity, mass, momentum, and torque, on the grip forces necessary for successful prevention. It was found that in a blocked presentation, as the cylinder mass increased, the grip and load forces involved in lifting it also increased (Johansson and Westling, 1984). While there was a trend for grasping forces to increase as cylinder velocity increased, this observation was not shown to be statistically significant. However, as the cylinder velocity increased so did the rate of force production when contacting and lifting the cylinder. The
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Fig. 3. Grip force and the transient torque values are plotted as a function of time for three representative trials for the 50 g, 0.457 m/s condition, and the 200 g, 0.114 m/s condition. The momentum value for both of these conditions was 22.8 gm/s. Grip force is shown by the solid black curve, the torque curves are dotted, and the dashed horizontal line is placed at the peak grip force of the plots for the 50 g, 0.457 m/s condition to serve as a reference. Panels A and B provide examples of trials where the torques for the two conditions were similar resulting in similar grip forces. In panel D, the trial (200 g, 0.114 m/s) with the high torque value has a corresponding higher grip force compared to panel C. In panel E, the opposite pattern was seen. In the 50 g, 0.457 m/s condition, a high transient torque value was observed and subsequently there was a higher grip force in comparison to panel F.
Table 2 Results of multiple regression analyses, where the predictor variables used were subject (S), cylinder mass (M) (g), cylinder velocity (V) (m/s), linear momentum (LM) (gm/s), and peak torque (Trq) (Nmm)
1 2 3
Model
R2
F (df)
GF=0.51+0.38S+0.02LM+0.36Trq+E GF=1.45+0.39S+0.01 M+0.002 V+0.002LM+0.35Trq+E GF=1.38+0.39S+0.01 M+0.002 V+0.35Trq+E
0.42 0.43 0.43
(3, 68)=16.90 (5, 66)=10.06 (4, 67)=12.76
observation that the actual generation of forces is influenced differentially by cylinder motion in comparison to the timing of force production, is similar to the observation by Mason and Carnahan (1999) that finger aperture size and timing are affected differentially when grasping moving cylinders. There may be independent mechanisms for grasp control that are responsible for the
timing versus the magnitude of associated muscular impulses. The results showed that as cylinder mass increased, grip force also increased. While there was a trend for cylinder velocity to show influence on grip force, there was no statistically significant effect. However, the multiple regression analysis chose the model that included the momentum of
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the cylinder a more parsimonious predictor of grip force than a model that included mass instead of momentum. Thus, while the effects of velocity were not statistically significant in the ANOVA, velocity did contribute in some form to grip force, as evidenced by the significant contributions of momentum (which is a product of cylinder velocity and mass). These data support the proposal made by Turrell et al. (1999) that momentum is an important variable that is represented in anticipatory models of force control (Johansson and Cole, 1994; Wolpert, 1997). The results of this study showed that the momentum of a moving target will influence the forces generated at the fingers during grasping. Thus, there is a larger potential for low-impact stress related injuries with repeated exposure to manual contact with faster/heavier moving objects. Thus, while increasing assembly line speed might speed up overall production, it could lead to increased worker injury. To help offset this potential for injury, increased assembly line speed could be offset with objects of smaller masses being manipulated.
Acknowledgements This research was supported by the Natural Sciences and Engineering Research Council of Canada.
References Carnahan, B.J., Norman, B.A., Redfern, M.S., 2001. Incorporating physical demand criteria into assembly line balancing. IEE Transactions 33, 875–887.
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