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NextPublishing 超原稿用紙（横組）　2016/4/1 版

Unsteady hydrodynamic forces acting on a robotic arm and Its flow field during the crawlHideki TAKAGI, University of Tsukuba, Tsukuba, Japan

Motomu NAKASHIMA, Tokyo Institute of Technology, Tokyo, Japan

Takashi OZAKI, SHIMANO INC., Osaka, Japan

Kazuo MATSUUCHI, University of Tsukuba, Tsukuba, Japan

Abstract— This study aims to clarify the mechanisms by which unsteady

hydrodynamic forces act on the hand of a swimmer during a crawl stroke.

Measurements were performed for a hand attached to a robotic arm with five

degrees of freedom independently controlled by a computer. The computer was

programmed so the hand and arm mimicked a human performing the stroke.

We directly measured forces on the hand and pressure distributions around it at

200 Hz; flow fields underwater near the hand were obtained via 2D particle

image velocimetry (PIV). The data revealed two mechanisms that generate

unsteady forces during a crawl stroke. One is the unsteady lift force generated

when hand movement changes direction during the stroke, leading to vortex

shedding and boundary vortex created around it. This boundary vortex

circulation results in a lift that contributes to the thrust. The other occurs when

the hand linearly moves with a large angle of attack, creating a Kármán vortex

sheet. This sheet alternatively sheds clockwise and counterclockwise vortices,

resulting in a quasi-steady drag contributing to the thrust. We presume that

professional swimmers benefit from both mechanisms. Further studies are

necessary in which 3D flow fields are measured using a 3D PIV system and a

human swimmer.

Key words: Competitive swimming, Flow visualization, 3D PIV

1. Introduction

The importance of unsteady phenomena in human swimming has been emphasized in previous studies (Sanders, 1999; Toussaint et al.,

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2002) , hence we know that quasi-steady hydrodynamic theory is insufficient to describe the mechanisms by which humans propel themselves through water. To address such problems, computational fluid dynamics (CFD), including the effects of unsteady fluid flow, has been making a major contribution to understanding hydrodynamic phenomenon when the swimmer was moving actively either on the surface or underwater (Von Loebbecke et al., 2009; Dabnichki, 2011). Particle image velocimetry (PIV) has also proven to be a powerful tool for measuring the actual flow fields around human swimmers. Based on PIV measurements, Matsuuchi et al. (2009) have reported that a pair of counter-rotating vortices might play an important role in generating unsteady fluid forces, and Hochstein and Blickhan (2011) have found that vortices generated in the region of strongly flexing joints are suitable to enhance propulsion; this process is known as vortex recapturing. Combining the results from CFD and PIV should help in visually and theoretically understanding complicated hydrodynamic mechanisms. However, actual experiment data, such as for forces and pressures, are also valuable for verifying CFD results and interpreting PIV images. Therefore, in a previous study, we conducted experiments in which we directly measured hydrodynamic forces, pressure distributions, and flow fields around a hand attached to a robotic arm (Takagi et al., 2013). In that work, simple 2D hand motions were the subject for study; nevertheless, a significant unsteady hydrodynamic phenomenon was observed that reveals the behavior of certain kinds of vortices play an essential role in generating substantial unsteady hydrodynamic forces. In this study, we used a robotic arm and PIV to clarify the mechanisms by which unsteady forces are generated during 3D crawl-stroke-motions. By analyzing the 3D motions, it is expected that actual propelling mechanisms can be elucidated and the findings will contribute to an improvement of swimmers’ technique.

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2. Method

2.1. Robotic arm and hand modelsA robotic arm that consisted of a trunk, shoulder, upper arm, forearm, and hand (Takagi et al., 2013) was used. The robotic arm had five degrees of freedom (DOF), which were driven by three motors housed in the trunk and two motors housed in the upper arm and forearm. Two hand models were fabricated from a silicon-based material (Takagi et al., 2013). One hand (Hand 1) was used to measure hydrodynamic forces via flow visualization, and another (Hand 2) was used to measure pressure distributions during stroking motions. Eight pressure sensors were embedded in Hand 2 to measure the pressure distribution on its surface (Fig.1).

2.2. Definitions of the coordinate system and technical termsThe origin of the global coordinate system was set at the center of the shoulder joint, as shown in Fig. 1. The x-direction was parallel to the main flow, the z-direction was upward and perpendicular to the main flow, and the y-direction was normal to the x- and z-directions. In this study, the following successive phases during one underwater stroke were defined by reference to Maglischo (2003). Downsweep is the phase during which the hand enters the water and moves outward/downward until the hand reaches the local maximal value of the y-coordinate. Insweep is the phase during which the hand’s moving vector (Uh) changes direction to the centerline of the body until the hand reaches the local maximal value of the z-coordinate. Upsweep is the phase during which Uh changes direction to outward/upward until the hand leaves the water.

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p1 p2 p3 p4 p5 p8p6 p7

Mirror

Flume

PCPulsegenerator

CCD camera

Load cell

Flow direction YAG laser

Robot arm

Hand

0.95m

z

xy

Pressure sensors

0.36, 0.46, 0.56 m/s

Fig. 1 Schematic of experimental devices and definition of the global coordination system

2.3. Particle image velocimetry (PIV)Two-component PIV was used to visualize flow around Hand 1. An Nd-YAG laser (Solo PIV 120 XT; New Wave Research Inc., USA) was used and a wide range of hand motions (0.5 m × 0.5 m) were covered. Nylon particles of 50 μm diameter (DAIAMID 2157; Daicel-Evonik Ltd., Japan) were used as tracers. The particle displacements (Δx, Δy) that occur during a short time Δt determine velocities byu = Δx ⁄ Δt , v =Δy ⁄ Δt (1)where (u, v) are the components of particle velocities in the x- and y-directions, respectively. In the present experiment, Δt was set to 1 ms.The vorticity was obtained to study the generation of forces that can be attributed to vortex generation and shedding. Vorticity is the measure of the rotational magnitude of a small fluid element or that of a vortex (Matsuuchi et al., 2009). The component normal (ζ) to the

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measured (x–y) plane is defined asζ = ∂u ∕ ∂y − ∂v ∕ ∂x (2)Computer-generated maps of vorticity and velocity around the hand were obtained every 67 ms by a cross-correlation-based two-component PIV algorithm (Sakakibara et al., 2004).

2.4. Reproduction of human swimming motionAn international-level female swimmer was used as a model, kinematic data of the motion of her right upper limb during the stroke were captured, and the data were loaded into the swimming human simulation software Swumsuit (Nakashima, 2007). Through Swumsuit, the robotic arm is computer controllable in the five independent DOFs to reproduce the swimmer’s motion, as much as possible. The motion was highly reliable (the error between the measured angle and the commanded angle was within 5%) and accurate data for forces were obtained (Nakashima and Takahashi, 2012). Since the reproduced hand path looked like an “S”, we call it Stroke S. We also modified the motion of Stroke S to make its trajectory more straightforward during Insweep and to reduce fluctuations in y-coordinate values; we call this Stroke I. The ranges of motion and durations from when the hand entered the water until it left the water were the same for both strokes S and I.

Table 1 Mean propulsive forces acting on the hand during a whole stroke movement

2.5. Data acquisition of forces, flow visualization, and pressure distributionsThe robotic arm was fixed above the measuring section with a 2D load

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cell (LSM-B-SA1; Kyowa Electronic Instruments Co., Japan), as shown in Fig. 1. The constant flow velocity (Uc) was set to one of three different values: 0.36, 0.46, or 0.56 m/s. The maximum Reynolds numbers for strokes S and I were 1.48 × 105 and 1.31 × 105, respectively.3D hand positions were calculated from the data obtained from position sensors. Data for positions and forces were sampled at 200 Hz and stored on the PC. By simultaneously recording these data and the trigger signal from the PIV system, all data related to hand displacement, hydrodynamic forces, and flow visualization around it were synchronized. To assess hydrodynamic forces acting only on the hand (Hand 1), the force acting on the robotic arm without the hand was measured before experimentation and then subtracted the force without the hand from that with the hand. After the hydrodynamic force measurements and flow visualization experiments, pressure distributions were measured by using Hand 2. This enables us to discuss relationships between pressure distributions and changes in the flow field. All conditions were similar to the first experiment; for example, the pressure data were sampled at 200 Hz.

3. Results

The largest thrust force was observed at Uc = 0.36 m/s, and in both stroke patterns, the thrust force peaks decreased with an increase in Uc. Thrust forces in Stroke S show bimodal peaks; the larger peaks occur in the latter part of the motion when the hand was switching from Insweep to Upsweep. In contrast, Stroke I shows single peaks in thrust forces near the middle part of the motion. The highest peaks in strokes S and I were 17.5 N and 27.5 N, respectively. Both stroke patterns exhibited negative thrust forces in the last parts of the motion, which correspond to Upsweep phases.

For Stroke S, when thrust forces reached maximum values,

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the hand changed from Insweep to Upsweep, a clockwise vortex was shedding from the thumb side due to the change in the hand’s direction of movement. This shedding vortex caused a new fluid circulation around the hand occurred (See Fig.2). At that time, a decrease in pressure over the dorsal side of hand was observed. For Stroke I, when the peak thrust force occurred, V reached its maximum, a Kármán vortex street was generated from the thumb or finger side. At that time, the pressure on the palm side had large positive values, while on the dorsal side the pressures were negative though not large absolute values.

Uh

UcVLift

Stroke S

--

Uh

UcV

+

Drag

+

+

α

α

Thumb

Littlefinger

Stroke I

Fig. 2 Conceptual diagrams of hydrodynamic forces acting on the hand during Stroke S (upper

panel) and Stroke I (lower panel).

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4. Discussion

In this study, hydrodynamic forces, pressure distributions, and flow visualizations were measured during the crawl stroke using a robotic arm. We adopted two types of crawl strokes S and I, but we did not focus most of our attention on comparison. Although the peak thrust force in Stroke I was larger than that in Stroke S, the inferior-to-superior relationship would change depending on conditions; therefore, we focused on differences in the mechanisms for generating hydrodynamic forces acting on the hand.

To provide an easy-to-understand explanation for the mechanism of generating hydrodynamic forces during the crawl stroke, conceptual diagrams were constructed and are shown in Fig. 2. In the case of Stroke S (upper drawing), a vortex was shed from the hand when it changes from Insweep to Upsweep. Before shedding the vortex, the thumb side was the leading edge and the direction of the bound vortex was clockwise; after shedding, the direction of the bound vortex becomes counterclockwise, in accordance with Kelvin’s circulation theorem. By adding this circulation to the moving velocity, the surface velocity increased, the surface pressure decreased, and a lift force was produced. At that time, the leading edge was the little-finger-side, and the resultant flow (V) was inward from the little-finger-side, as shown in the figure. Since the lift force acts perpendicular to V, the lift force must contribute to an increase in the thrust force. This phenomenon is known as the unsteady mechanism of force generation that insects apply for flying (Dickinson, 1996).In the case of Stroke I (lower drawing in Fig. 2), when the hand moved in a linear manner with a large angle of attack, a Kármán vortex street was generated, and clockwise or counterclockwise vortices were alternately shedding from it. At that time, the pressure on the palm side was large and positive, and the pressure difference between the palm and dorsal sides increased, producing a drag force. This drag

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force must contribute to an increase in the thrust force.We have been able to unravel parts of the hydrodynamic mechanisms during the crawl stroke, but we also recognize some limitations. For example, the resultant flow vectors relative to the hand (V) achieved by the robotic arm did not reach 1.7 m/s at the maximum; in fact, they were approximately half of those in actual swimming motions (Maglischo, 2003). In addition, the robotic arm had no degree-of-freedom at the wrist joint, thus palmar flexion and dorsal flexion of the wrist could not be reproduced. These differences and defects were due to limitations on the output power and driving mechanisms of the robotic arm. Only 2D flow-field images during crawl-stroke-motions were obtained in this study. Since hand movements are 3D, it would be better to obtain 3D vortices and velocity distributions; this has not yet been done due to limitations on the number of CCD cameras and on the performance of the software.

5. References

Dabnichki, P., 2011. Unsteady fluid mechanics effects in water based human locomotion. Mathematics and Computers in Simulation 82, 471-482.

Dickinson, M.H., 1996. Unsteady mechanisms of force generation in aquatic and aerial locomotion. American Zoologist 36, 537-554.

Hochstein, S., Blickhan, R., 2011. Vortex re-capturing and kinematics in human underwater undulatory swimming. Human Movement Science 30, 998-1007.

Maglischo, E.W., 2003. Swimming Fastest. Human Kinetics, Champaign, IL.

Matsuuchi, K., Miwa, T., Nomura, T., Sakakibara, J., Shintani, H., Ungerechts, B.E., 2009. Unsteady flow field around a human hand and propulsive force in swimming. Journal of Biomechanics 42, 42-

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47.Nakashima, M., 2007. Mechanical study of standard six beat front

crawl swimming by using swimming human simulation model. Journal of Fluid Science and Technology 2, 290-301.

Nakashima, M., Takahashi, A., 2012. Clarification of Unsteady Fluid Forces Acting on Limbs in Swimming Using an Underwater Robot Arm (Development of an Underwater Robot Arm and Measurement of Fluid Forces). Journal of Fluid Science and Technology 7, 100-113.

Sakakibara, J., Nakagawa, M., Yoshida, M., 2004. Stereo-PIV study of flow around a maneuvering fish. Experiments in Fluids 36, 282-293.

Sanders, R.H., 1999. Hydrodynamic characteristics of a swimmer's hand. Journal of Applied Biomechanics 15, 3-26.

Takagi, H., Nakashima, M., Ozaki, T., Matsuuchi, K., 2013. Unsteady hydrodynamic forces acting on a robotic hand and its flow field. Journal of Biomechanics 46, 1825-1832.

Toussaint, H.M., Van Den Berg, C., Beek, W.J., 2002. Pumped-up propulsion during front crawl swimming. Medicine and Science in Sports and Exercise 34, 314-319.

Von Loebbecke, A., Mittal, R., Mark, R., Hahn, J., 2009. A computational method for analysis of underwater dolphin kick hydrodynamics in human swimming. Sports Biomechanics 8, 60-77.

White, F.M., 1999. Fluid Mechanics, Fourth Edition ed. McGraw-Hill, Boston, Il.

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