A Novel Stairway-Handrail Rehabilitation System Static and Dynamic tests: Quantification of 3D Handrail Forces

Shing-Jye Chen & Yuan-Hsing Shih

Medical Device Innovation Center (MDIC) National Cheng Kung University

Tainan, Taiwan shingjychen@gmail.com

Abstract—Stair negotiation demands greater

muscular strength in challenging for those who have lower limb impairments while climbing stairs. To overcome the challenges on stairs, stair handrail device has been designed for rehabilitation in providing necessary handrail gripping strength for stair negotiation safety in concerns with climbing stability enhanced by a modulation of lower limb reflex. Thus, the purpose of this study was to quantify 3D handrail gripping forces necessary for climbing safety in a newly designed stairway-handrail rehabilitation system. Potential noises of the stairway-handrail system were detected and corrected by a means of implementing static weight loading and dynamic pendulum tests on the handrail as well as dynamic handrail gripping force measurements while subjects negotiated the stairway. The findings suggest that measurements of the stairway handrail forces were quantifiable and validated after the forces were filtered, corrected and examined for the subjects who negotiated the stairway and grasped the handrail of the stairs. Therefore, the current novel design of the instrumented stairway handrail system would be able to rehabilitate the subjects impaired with lower limbs while climbing and negotiating the stairs and to further quantify a critical need of how an assistive handrail affects lower limb biomechanics for a safe stair negotiation.

Key words—Stairway negotiation, stair ascent, handrail force, gripping force, force plate, biomechanics.

I. INTRODUCTION Stair negotiation is one of the most common activities of

daily life, and it demands greater muscular strength in lower limbs, especially for those who are prone to a higher incidence of falls and trips on stairs [1]. However, when the elderly and individuals have a joint replacement or being obesity, osteoarthritis, and neuromuscular dysfunction in their lower limbs, they often encounter potential difficulties in climbing stairs. To overcome the potentials of climbing and walking on stairs, an assistive handrail device has often been used as a critical component for stairs safety, specifically rehabilitation for elders who experienced history of falls [2]. In stair climbing studies, adequate handrail gripping strength in elderly was revealed being

necessary for a safe negotiation on stairs [3], and a grip of an assistive stairway-handrail modulated a lower limb reflex to enhance stair climbing stability [4].

Currently, a newly developed stairway instrumented to directly measure handrail forces in 3D have been neither transportable [5] nor compact and less weighted [6]. These instrumented stairways are purposely designed and limited for laboratory studies, but not for rehabilitation uses. To increase functionality of a stairway, a novel design of stairway able to be conveniently relocated and transported to various locations, especially for physical rehabilitation, is valuable and applicable as a result of its increased accessibility for patients who require rehabilitation on stairs as well as who use stairs for a home-based exercise program.

Up to date, a rehabilitation stairway equipped with a handrail force measuring system being transportable has not been found yet. Thus, a novel designed stairway handrail system was constructed to quantify necessary handrail gripping forces of subjects while negotiating stairs. The purpose of this study was to examine a stairway system instrumented with 3D handrail force measurements by first detecting noise frequency of the handrail before and after noise reducers (e.g. rubber washers and foam pads) placed in the system and second by detecting cross talks of forces among force plates embedded in the stairway. Third, in measuring 3D handrail forces of healthy young subjects while on stairs after noise of the handrail was reduced and filtered. Then, the handrail forces were corrected using the early established force error correction regressions. The novel stairway was designed to be transportable and tested in the Biomechanics motion laboratory at University of Nebraska (UNO) at Omaha, NE, United States.

II. INSTRUMENTED STAIRWAY HANDRAIL SYSTEM A transportable four-step staircase (20.4 cm in step height;

28.0 cm in tread length) was constructed by using lightweight rigid aluminum beams in supporting the stairway system. For the first three steps from level ground to top stairs, each step was embedded with one 0.47 x 0.51 x 0.08 meters (W x L x H) AMTI force plate (OR6-7-1000) and enclosed by separate woods for aesthetic visual purpose (see Fig. 1a).

The instrumented handrail consisted of two independent lightweight tubular steel rails or pipes designed to support subjects climbing on the stairs. Each handrail was a closed

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loop design and directly clamped to each end of a long stiff metal beam (1.2 x 0.2 x 0.3 in meters; mass: 44 kg). To securely fasten each side of the handrail to the long support beam, a customized metal blocker (0.15 x 0.12 x 0.04 in meters; mass: 5kg) was designed to fit and clamp to each tubular rail. The blocker and tubular rail were clamped metal by metal to each other and screwed securely to the end of the support beam with four steady metal bolts (0.105 m in length x 0.025m in diameter; see Fig. 1b).

To measure 3D handrail forces of the rail, the supporting beam to which the rail was attached was directly placed anchoring to the top center of an AMTI force plate (OR6-6-1000; see Fig. 1c). Each orientation of the force plate coordinate system was with respect to a global coordinate of the stairway (see Fig. 1a; X axis in anterior posterior (AP) direction, Y axis in medial-lateral (ML) direction, and Z axis in vertical (V) direction).

III. STATIC TEST OF 3D HANDRAIL FORCE MEASUREMENTS Prior to testing the current handrail system being grasped

by subjects on stairs, two designated locations (i.e., lower H1 and upper H2, see Fig. 1a) of the right handrail were spotted. Each spotted handrail was close to a natural handrail grasping area of each subject while gripping handrail during ascending and descending. The handrail grasping areas were assumed to be symmetrical on both sides of the handrails. During a static testing, each grasping spot was loaded with a suspended known static weight being pulled via a custom pulley system into anterior-posterior (AP), medial-lateral (ML), & Vertical (V) directions, relatively to the global x, y, & z axis. An incremented weight of 34N, 156N, 178N, 200N and 223N, respectively, was tested. At least three static loading trials were collected at each grasping spot.

IV. DYNAMIC TEST OF 3D HANDRAIL FORCE MEASUREMENTS

To test potential noise frequency of the stairway-handrail system, a known weight of a 90N object was suspended on each of the H1 and H2 handrail gripping spots and swung for a pendulum moving into a forward-backward or side-by-side direction. Both swinging directions were mainly tested because of a smaller grasping handrail force found on stairs and a relatively greater noise seen in these directions in comparing to those of the vertical direction.

Since potential noises of the handrail system were found existing among the metals of the tubular handrail, clamping blocker and steel support beam, some noise reducers such as rubber washers (3.5mm in thickness) and a 2cm thick deformable foam pad were placed in each bolt and padded between the metal contacting areas, respectively. Noise reduction in handrail forces during the pendulum test was detected. Potential cross-talks of the step forces and handrail forces measured among force plates were examined when subjects were asked to fast ascend and descend the stairway while grasping a right sided handrail.

V. DATA COLLECTION OF STAIC AND DYNAMIC TESTS Each orthorgonal 3D handrail force collected during both

static and dynamic tests was acquired by a data acquisition system (EvaRT 5.0, Motion Analysis Co, Santa Rosa, CA) as well as 3D ground reaction forces (GRFs) measured from the steps while the subjects were asked to climb on the stairs. Each force plate embedded in the stairway-handrail system was synchronized and sampled at 600Hz for 5 seconds. Each raw force signal was amplified and filtered initially by an AMTI MSA-6 amplifier with built-in 1000 Hz low pass filter.

During the static weight loading test, a regression line of handrail force error corrections was established in each force direction using polynomial equations. Each force correction was calculated based on the corresponding force regression that was correlated between each given known weight and force differences or errors. The force errors were calculated between a given true weight and its output measured force of the handrail system. The output measured force was an averaged force of three trials of each given testing load for each direction. During the dynamic test of the suspended object swinging on the handrail, a power density frequency (PDF) of the measured handrail forces was calculated to detect noises before and after the noise reducers were placed [7]. A custom MatLab 6.0 program (MathWorks, Inc) was used to calculate the PDF.

Fig.1. a) A side view of the instrumented handrail stairway system. A 90N suspended object was loaded at each lower and upper location of the handrail (H1, and H2, respectively), b). The steel tubular handrail is clamped to each attached end of the support beam with a metal blocker holding by four steady bolts. c) A top view of the long rigid metal support beam. The beam is screwed tightly to the top surface of the force plate specifically used to measure handrail forces in 3D.

a).

c).

c

Support beam

Handrail Force Plate

b).

Clamping metal blocker

H2

H1

P1

P2

P3

y (ML)

x (AP) z (V)

Right Handrail

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1st Grip 2nd Grip

Fig. 3. Filtered 3D Handrail forces corrected by the error correction regressions of a representative subject during ascent while gripping handrail in success twice on stairs

AP

ML

V

AP

ML V

Fig. 2. Unfiltered and filtered 3D handrail forces of a representative subject during stair ascending while gripping handrail in success twice on stairs.

Fy(ML)

Fx (AP)

Fz(V)

1st Grip Fx (AP)

Fz(V)

2nd Grip

Fy(ML)

The other dynamic test of the handrail system was performed to quantify the handrail forces necessary for climbing safety when each of a total five healthy young subjects (N=5) was asked to ascend the stairway grasping a right sided handrail. Ascending pace was controlled by a metronome set at 120 steps/min (i.e., approximately 0.6 m/s) [8] with one foot on each step, a step-over-step climbing strategy. Meanwhile, two consecutive handrail grasps were performed during ascent. The areas of grasping were the same spots being tested in the static and dynamic tests. Each measured handrail force was initially filtered by the 4th order zero lag Butterworth lowpass with a cut-off frequency 3.57 Hz and followed by a correction of the filtered forces based on the previously established regression lines. Cross talks of all forces measured from the stair steps and handrail were examined.

VI. RESULTS The findings of the static and dynamic tests for 3D

handrail force measurements provide in supporting necessary climbing safety quantifications of the instrumented transportable stairway handrail system.

A. Regression lines of handrail force error correction in 3D The error correction of the handrail force of each

direction is expressed in the following polynomial equations (see Eq.1, 2 and 3): Y- a predicted error output and X- a given known weight input for each direction of the AP, ML and V with respect to the global x, y and z axes, respectively. � is a correlation of coefficient showing a strength relationship between the Y and X.

YAP = - 0.0017X2 + 0.8867X - 37.77. �2 = 0.55 (1) YML = - 0.0005X2 + 0.5662X - 19.60. �2 = 0.64 (2) Y V = - 0.0002X2 + 0.0597X - 2.75. �2 = 0.31 (3)

The �2 of the YAP and YML regression lines shows a

moderate strength of force correction between the predicted error (Y) and the known weight (X), but a weak �2 for the YV regression.

B. Power density frequency before and after noise reducers placed during dynamic pendulum test Before and after the noise reducers (e.g., rubber washers

and padding foams) were used, a reduced PDF of the measured handrail forces was shown mainly in both AP and ML directions, but not in the V direction.

C. Unfiltered and filtered handrail forces prior to implementing force error correction for stair ascent Figure 2 shows a general trend of handrail forces in each

direction (Fx- AP, Fy-ML, and Fz-V) being superimposed for both unfiltered and filtered forces. The upward V handrail reaction force shows the greatest value, compared to that of the other forces: 1) a forward AP pushing reaction force and 2) a medial inward ML pushing reaction force. The 1st vertical grip force shows two main peaks and one peak in the 2nd grip. Both AP and ML forces also show one major peak consistently occurring in an approximate half way of handrail force production.

D. Filtered handrail forces before and after error correction implemented for stair ascent Figure 3 shows the filtered handrail forces in each

direction being corrected by the error correction regression lines. Both AP and ML forces show a greater force error correction than that of the V force for both handrail grips, specifically a 4N, 12N and 10N force correction made in the first rail grasp in the V, AP and ML directions, respectively. No cross-talks of the force outputs measured from force plates of the stairway system were detected.

Handrail force in each direction

H1 (lower)b before/after

H2 (upper)b before/after

APa 6.5 /1.5 7.5 / 0.7 MLa 6.5/ 0.7 4.5 / 2.0 Va 18 / 20.5 13.5/ 19.0

a. AP (anterior-posterior), ML (medial-lateral) and V (vertical). b. Unit: Hz

Table. 1. Handrail noise detection before and after noise reducers placed in the stairway handrail system

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VII. DISCUSSION The current findings of the novel transportable

instrumented stairway handrail system have shown that the 3D handrail forces being filtered, corrected and examined were quantified necessary for a safe stair climbing in healthy young subjects who negotiated the stairway while grasping handrail. The detected noises of the handrail system were able to be reduced mainly in both AP and ML forces, but not in the V force. Both AP and ML force measurements with the reduced noises may become more reliable than the V force when the stairway handrail system was used. The least noise reduction of the V force could be due to the least effective pendulum effects while given to and swinging into the AP and ML directions for testing the handrail system.

In the dynamic test of stair ascent with two consecutive handrail grips, the least force error correction was detected in the vertical direction, but a greater error correction found in both AP and ML directions. The force error corrections in each direction suggest that a quantifiable force in supporting a body weight of the subjects was mainly seen in the vertical direction in comparison to the other pushing reaction forces in the AP and ML directions while grasping the handrail twice during stair ascent.

Although a similar griping handrail pattern was seen between two consecutive grips of each direction in supporting and pushing the subjects on stair ascent, the two major peaks of the supporting force in the first grip may reveal a greater challenge for the subjects in negotiating stairs when climbing from ground floor to the first stair, being compared to a stair to stair transition during the 2nd handrail grip. In addition, the free cross-talks among the force plates indicate each force plate independent to one another so that the plate was well installed and isolated in each stair of the stairway and handrail system. In conclusion, the current instrumented stairway handrail system is ready for testing human subjects in rehabilitation by climbing and negotiating the stairs and for further quantifying handrail forces of subjects who need for an assistive handrail support necessary for a safe climbing on stairs.

ACKNOWLEDGMENT The author SJ. C. thanks Dr. Stergiou, N. at Nebraska Biomechanics Core Facility, University of Nebraska (UNO) at Omaha, NE, United States in providing great supports and the instrumented stairway, and also thanks to the UNO University Committee on Research and Creative Activity (UCRCA) faculty grant support.

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