- Email: [email protected]
Development and testing of a modular strain measurement clip
ARTICLE IN PRESS
Journal of Biomechanics 36 (2003) 1669–1674
Development and testing of a modular strain measurement clip Gabrielle Whana, John Phillipsa, Stacy Bullocka, R. John Runcimana,*, Simon Pearceb, Mark Hurtigb b
a School of Engineering, University of Guelph, Guelph, Ont. N1G 2W1, Canada Ontario Veterinary College, University of Guelph, Guelph, Ont. N1G 2W1, Canada
Accepted 7 April 2003
Abstract A novel, multi-use, low-stiffness and low-cost transducer for measuring in vitro strains has been developed and tested. Currently available strain measurement methods are either too expensive, too complicated or too inflexible for multi-use strain measurement. The stainless-steel modular strain measurement clip introduced here was instrumented with four 350 O axial strain gauges in a full Wheatstone bridge configuration to take advantage of commonly available strain gauge amplifier equipment. Adjustable extension arms were designed to allow greater application versatility. The clip was calibrated and produced a linear response (R2 > 0:99) over a minimum of 1.04 mm at high amplifier gain. With reduced amplifier settings, testing showed a linear response over a range of 30.5 mm (R2 > 0:99). Clip stiffness was 0.6 N/mm of extension arm tip displacement for minimal instrumentation artifact. A validation test was conducted through a comparison of strain clips, surface-mounted strain gauges and theoretical strain in an aluminium rod subjected to axial tensile loading. The two measurement techniques were used to determine the modulus of elasticity of the aluminium rod. Results were within 6% of the known modulus of elasticity for aluminium. A comparative biomechanical test was also performed on an equine third metacarpal specimen. The traditional bonded strain gauging method produced similar results as the new strain clip, but failed to measure ultimate strains since all strain gauges failed prior to specimen failure. Further investigations into the multiple uses of the clip are underway and recommendations for future versions of the clip are given. r 2003 Elsevier Science Ltd. All rights reserved. Keywords: Strain measurement; Bone; In vitro; Extensometer; Stress
1. Introduction Strain response of the skeletal system to external forces has been studied in a wide variety of applications (Roberts, 1966). This phenomenon has usually been measured using electrical-resistance strain gauges. Strain gauges have been implanted in vitro and in vivo on many different bone types and locations (Davies et al., 1993; Les et al., 1998; Schneider et al., 1981; Turner et al., 1975). Unfortunately, the use of gauges on bone has many associated problems. Successful strain gauging of a material is dependent on an intimate bonding interface. As bones are porous and saturated with fluid, preparing a surface for installation is difficult. Body fluids are also *Corresponding author. Tel.: +1-519-824-4120; fax: +1-519-8360227. E-mail address: [email protected] (R.J. Runciman).
extremely corrosive, and are able to permeate or destroy a wide variety of protective coatings on the gauge (Roberts, 1966), even in vitro. Other problems associated with strain gauges are their one-time, short-term use, and the fact that they cannot normally be used to specimen failure. For these reasons, some researchers have investigated alternatives for measuring bone deformation including instrumented staples and grip-mounted extensometers. Several limitations exist with these methods. First, instrumented staples can be damaged during insertion and the inherent rigidity of the staple will alter the stress and strain distribution in the bone. For grip-mounted extensometers, relative motion between bone and grips, cost and size are all drawbacks. This paper introduces a novel, multi-use, low-stiffness and low-cost transducer for in vitro strain measurements. The versatility of this design allows for the measuring of large strain deformations through to
0021-9290/03/$ - see front matter r 2003 Elsevier Science Ltd. All rights reserved. doi:10.1016/S0021-9290(03)00173-8
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G. Whan et al. / Journal of Biomechanics 36 (2003) 1669–1674
Fig. 1. Schematic of exploded view of clip and photograph of clip mounted to aluminium rod during test. The strain clip composed of a ‘‘c’’ shaped stainless-steel clip, thickness of 1 mm, instrumented with four 350 O axial strain gauges (two bonded to the concave and two to the convex side of the end web) wired in a full Wheatstone bridge configuration. A pair of modular extension arms with knife edges have been added to facilitate the interaction with the test sample. The bottom arm acts as a potentiometer to allow for bridge balancing without the need for amplifier adjustments. A pair of rings with screws is used to mount the clip to the test sample, dimensions in mm.
specimen failure. This was accomplished through the design of a clip instrumented with strain gauges (hereby referred to as a strain clip) that utilises adjustable and replaceable arms, and for the application documented here, a pair of rings with screws serving as the bone/clip interface. This study explores the calibration and use of a modular strain clip in comparison to surface-mounted strain gauges and theoretical strain measurements on an aluminium bar. The strain clip was also assessed through its application to a section of in vitro bone under load.
2. Methods The clips were fabricated from stainless steel to the dimensions illustrated in Fig. 1. Two stainless-steel rings were designed to interface the test sample with the clips. The test sample was secured in the rings with two sharply pointed 6/40 stainless-steel screws. Adjustable steel extension arms were fabricated for the clips. The arms were shaped and attached to the clips with screws. One arm in each pair acted as a potentiometer by allowing the tip force to be adjusted, altering the stress and, therefore, the strain in the clip. This was used to make adjustments to the initial gauge reading without making amplifier adjustments and recalibrating. The tips of the extension arms were formed into knife edges to be snapped between threads of the adjacent screws.
During use, these knife edges articulated on the threaded portion of the screws. Four encapsulated 350 O axial strain gauges (MM CEA-06-250UN-350)1 were epoxy bonded in parallel to the inner and outer web of the strain clip following standard strain gauge application techniques (Vishay Measurement Group, 2001). Twenty-eight AWG PVC insulated lead wires were soldered to the gauges in a full Wheatstone bridge configuration. A protective coating of RTV silicone rubber was then applied to all four gauges. Clip calibration was accomplished using an adjustable height gauge fitted with threaded rods. Clip arms were placed between the height gauge and a second threaded rod mounted in a vise. Clip response was recorded for changes of 0.0254 mm (0.001 in) displacements determined by the height gauge (70.0127 mm). Bridge excitation and signal conditioning were accomplished using custom-built amplifiers (Analog Devices 2B30 modules) with an excitation voltage of 6 V and a gain of 10. Voltage output was recorded at 120 Hz using standard PC data acquisition software2 and a 16-bit A/D converter2. The voltage to displacement ratio for the clip was then determined using standard linear regression techniques.
1 2
Vishay Measurements Group, Raleigh, NC, USA. National Instruments, Austin, TX, USA.
ARTICLE IN PRESS G. Whan et al. / Journal of Biomechanics 36 (2003) 1669–1674
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Fig. 2. Bone used in the comparative biomechanical test. The sample was removed from the mid-diaphysis of an equine third metacarpal and shaped from a pillar to the above shape. Two axial strain gauges were bonded to the surface on the front and back of the sample as shown and wired as independent 1/4 Wheatstone bridge circuits. The region of interest was shaped to be 20 mm long, 5 mm wide and 5 mm deep.
The stiffness of the clip was also tested. The upper arm of the clip was fixed in a vise. A series of weights were hung from the end of the lower arm, and the resultant tip deflection was measured using the height gauge. A clip stiffness factor was then calculated. To evaluate the performance of the clip relative to bonded strain gauges, a comparative test was performed using a long cylindrical aluminium rod of constant diameter (81 cm length; 1.27 cm diameter) strain gauged with two surface-mounted axial gauges (Showa N11FA-10-120-11) oriented 180 to each other. Two clips were placed between screws fixed onto each side of the rod using the rings (see Fig. 1). The screws were aligned and secured in the middle of the bar and perpendicular to the longitudinal axis of the rod. The gauges were attached to the same custom-built signal conditioning amplifiers completing the Wheatstone bridge configuration set to an excitation voltage of 6 V and a low gain. The aluminium rod was subjected to axial tension to a maximum of 4 kN at a load rate of 2 mm/min in a universal electromechanical testing machine (Instron model 4204) instrumented with a 50 kN load cell. Aluminium rod load, clip output and gauge output were all sampled at 120 Hz using the same data acquisition system. Clip results were converted to strains using the previously determined calibration factor. Strains measured with the surface-mounted gauges were determined using shunt calibration techniques and standard formulae (Dally and Riley, 1978). Strains from the two gauges and from the two clips were each averaged to find the strain at the centre of the rod and to eliminate the effect of any unwanted bending in the rod. Strains from the two techniques were then used to produce stress–strain curves and calculate the modulus of elasticity for aluminium.
A comparative biological test was conducted by applying the strain clip to samples of bone from the mid-dorsal diaphysis of equine third metacarpals. Samples were shaped into a two-dimensional hour glass profile (Fig. 2) using an air-driven router outfitted with a 1/4 in up spiral router bit. Backside shaping was also done, yielding a testing region with a constant cross sectional area of cortical bone (25 mm2). Samples were instrumented with axial gauges on the periosteal and the internal surfaces (see Fig. 2). The stainless-steel rings were placed over the samples before being positioned in two custom-built Instron aluminium grips. The rings were arranged with a nominal gauge length of 15 mm, the screws were tightened into the bone sample and the strain clips were placed or clipped into position on the screw threads. Samples were subjected to a tensile load at a rate of 6 mm/min to failure. The clip, gauge and load output voltages were collected as previously described. Clip and gauge outputs were each averaged to calculate the strain at the centre of the sample. Results from both techniques were used to determine the modulus of elasticity for the bone sample.
3. Results Calibration of clips exhibited a linear voltage response to displacements over a range of 30.5 mm (R2 > 0:99). With amplifier settings as documented above, the working range of the strain clips was 1.04 mm and the calibration factors for the two clips ranged from 0.40 to 0.45 V per 0.0254 mm (0.001 in) displacement. R2 values for the linear regression were above 0.99. A typical calibration graph can be seen in Fig. 3. Clip stiffness was 0.6 N/mm of displacement.
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Fig. 3. Typical calibration curve for the clips. Each point represents a tip displacement change of 0.0254 mm. Amplifier settings were 6 V excitation with a gain of 10. Clip output was linear over the entire region (R2 > 0:99).
Fig. 4. Typical validation test results on an aluminium rod fitted with surface-mounted strain gauges and the strain clips.
In the validation test conducted on the aluminium bar, a modulus of elasticity of 73 and 65 MPa were calculated using data from the bonded strain gauges and the clips, respectively. The modulus of elasticity for aluminium is quoted as 69 MPa (Baumeister, 1978), yielding an error of 6% or less for each method. Sample results from this test can be seen in Fig. 4. For the comparative biomechanical study, output data from the strain gauges adhered directly to the bone were compared to the strain clip results. Results from the two methods predicted a modulus of elasticity of bone within 1% of each other at low stresses, as shown in Fig. 5. Strain gauge failure occurred at 3000 mm, well before sample failure at approximately 9000 mm.
4. Discussion The demand for strain information has pushed researchers to investigate numerous strain measurement
Fig. 5. Typical results from the comparative test on a small bone sample. The surface-mounted strain gauge failed between 2500 and 3000 mm. Ultimate strain of the bone sample could not be found using the strain gauges. The strain clips continued to measure strain in the sample to failure, at approximately 9000 mm. There was a difference of 1% between the two methods at the point of gauge failure during the test.
techniques. The use of a pre-instrumented clip to measure strain would reduce many of the complexities associated with bone strain measurements made using surface-mounted gauges, instrumented staples or dedicated strain devices, especially for in vitro testing and testing ultimate material properties. The clips introduced in this paper offer many advantages over previously developed measurement techniques. Surface-mounted strain gauges when appropriate are very expensive. The strain clips introduced here incorporate only four strain gauges and have been repeatedly used with no deterioration in performance. The use of the rings and screws allows for total reusability of the clips, as well as the option of precutaneous placement of the screws, simplifying the instrumenting procedure. The rings allow a lowartifact strain measurement with minimum impact on the bone stress field. The clip shape and anchor interface have been chosen to reduce instrument stiffness and associated artifacts while optimising sensitivity. Other researchers have investigated alternatives to bonded strain gauges for measuring bone strain (Arndt et al., 1999; Butterman et al., 1994; Ekenman et al., 1998; Boyd et al., 2001; Reilly et al., 1974). Most of these devices have been titanium staple type units with pre-bonded gauges. The design of this clip improves on the use of the titanium staple by reducing the rigidity of the instrumented device and eliminating unwanted stress field artifacts. Clip stiffness was 0.6 N/mm of tip displacement. Calculated values for a titanium staple with an elastic modulus of 115 GPa reveals about 45,000 N of force generated per mm displacement of the staple leg. When this staple is inserted into a material
ARTICLE IN PRESS G. Whan et al. / Journal of Biomechanics 36 (2003) 1669–1674
such as bone with a significantly lower elastic modulus, load sharing will occur between the staple and the bone. This load sharing will alter the stress distribution in the bone, and therefore the strain being measured. The amount of load sharing would vary with not only the relative difference in elastic modulus’, but also bone hardness, interface design, bone thickness, and staple insertion depth. To overcome the effects of load sharing, the staples have typically been calibrated using a proportional factor to correct the strain measured using the staple to that of a surface-mounted gauge placed under the staple. This time-consuming step is unnecessary with the clip presented here and adds to the ease of use. The advantage of a linear relationship between strain and output of a strain measurement device cannot be overlooked. Output from the strain clip was linear over a large range and can therefore be used in a wide variety of applications. For strain measurements in the biological samples as discussed here, the equipment was adjusted to the application to achieve a high sensitivity for small changes in strain. In order to measure strain on a biological sample, this application incorporates a set of extension arms with a knife-edge interface between the screws of custom-built rings. A variety of extension arms could be designed and implemented for different applications. Using modified arms, clips can be adapted for tensile and compression testing, variations in sample size and interface methods. During the comparative biomechanical test, the prediction of the modulus of elasticity was hindered by failure of the bonded strain gauges. In one test the bonded strain gauge failed almost immediately and in all tests the gauges failed prior to sample destruction. This is not uncommon with surfacemounted gauges. This type of failure with strain gauges hinders their application measuring ultimate strains in samples. Estimates from the data that were collected before the strain gauges failed agreed with the modulus of elasticity found using the output from the strain clips. In vivo use of the strain clips is limited by the clip bone interface. Bone screws were initially investigated but artifacts resulting from the bone screws made the results unreliable. The pair of rings used in this paper were designed to reduce artifacts and allow for a strain reading by averaging the two clips for small sample in vitro testing. Our laboratory use of the strain clips has allowed us to identify a number of improvements that could be made to the current design. Repeated use indicated that bridge wiring was susceptible to damage. The use of a lighter gauge wire and strain relief would improve the durability of the strain clips. The strain clips could also be constructed with a bias to facilitate either tension or compression type testing. Pre-straining the clip before
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bonding the gauges, either in compression or tension would improve the working range of the clip. This would specialise the clips for either compression or tension applications.
5. Conclusions The introduction of a multi-use, low-cost strain measurement system that is simple to produce will be of particular interest to biomechanical laboratories. The strain clip is highly versatile in its modular design. The bone testing application included here is an example of just one of the many applications for the strain clips. Replaceable extension arms, high linearity over a working range of 30.5 mm, and simple calibration are all characteristics that will lead to the use of these clips in a variety of future applications.
Acknowledgements The authors would like to thank Sean Smith, Peter Perk, and Bill Verspagen from the School of Engineering for technical assistance; and NSERC and Sunlight Medical Ltd., Israel for funding this research.
References Arndt, A., Westblad, P., Ekenman, I., Halvorsen, K., Lundberg, A., 1999. An in vitro comparison of bone deformation measured with surface and staple mounted strain gauges. Journal of Biomechanics 32, 1359–1363. Baumeister, T., 1978. Marks’ Standard Handbook for Mechanical Engineers, 8th Edition. McGraw-Hill, New York. Boyd, S., Shrive, N., Wohl, G., Muller, . R., Zernicke, R., 2001. Measurement of cancellous bone strain during mechanical tests using a new extensometer device. Medical Engineering Physics 23, 411–416. Butterman, G.R., Janevic, J.T., Lewis, J.L., Lindquist, C.M., Wood, K.B., Schendel, M.J., 1994. Description and application of instrumented staples for measuring in vivo bone strain. Journal of Biomechanics 27, 1087–1094. Dally, J., Riley, W., 1978. Experimental Stress Analysis. McGraw-Hill, New York. Davies, H., McCarthy, R., Jeffcott, L., 1993. Surface strain on the dorsal metacarpus of throughbreds at different speeds and gaits. Acta Anatomica 146, 148–153. Ekenman, I., Halvorsen, K., Westblad, P., Fellander-Tsai, L., Rolf, C., 1998. The reliability and validity of an instrumented staple system for in vivo measurement of local bone deformation. Scandinavian Journal of Medical Science and Sports 8, 172–176. Les, C., Stover, S., Taylor, K., Keyak, J., Willits, N., 1998. Ex vivo simulation of in vivo strain distribution in the equine metacarpus. Equine Veterinary Journal 30, 260–266. Reilly, D.T., Burnstein, A.H., Frankel, V.H., 1974. The elastic modulus for bone. Journal of Biomechanics 7, 271–275.
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Roberts, V.L., 1966. Strain-gage techniques in biomechanics. Experimental Mechanics 6, 19A–22A. Schneider, R., Mine, D., Gabel, A., Groom, J., Bramlage, L., 1981. Multidirectional in vivo strain analysis of the equine radius and tibia during dynamic loading with and without a cast. American Journal of Veterinary Research 43, 1541–1550.
Turner, A.S., Mills, E.J., Gabel, A.A., 1975. In vivo measurement of bone strain in the horse. American Journal of Veterinary Research 36, 1573–1579. Vishay Measurement Group, 2001. Interactive guide to strain measurement technology: gage installation applications. http:// www.vishay.com/brands/measurements group/guide/indexes/ tt index.htm. Vishay Intertechnology Inc.
Journal of Biomechanics 36 (2003) 1669–1674
Development and testing of a modular strain measurement clip Gabrielle Whana, John Phillipsa, Stacy Bullocka, R. John Runcimana,*, Simon Pearceb, Mark Hurtigb b
a School of Engineering, University of Guelph, Guelph, Ont. N1G 2W1, Canada Ontario Veterinary College, University of Guelph, Guelph, Ont. N1G 2W1, Canada
Accepted 7 April 2003
Abstract A novel, multi-use, low-stiffness and low-cost transducer for measuring in vitro strains has been developed and tested. Currently available strain measurement methods are either too expensive, too complicated or too inflexible for multi-use strain measurement. The stainless-steel modular strain measurement clip introduced here was instrumented with four 350 O axial strain gauges in a full Wheatstone bridge configuration to take advantage of commonly available strain gauge amplifier equipment. Adjustable extension arms were designed to allow greater application versatility. The clip was calibrated and produced a linear response (R2 > 0:99) over a minimum of 1.04 mm at high amplifier gain. With reduced amplifier settings, testing showed a linear response over a range of 30.5 mm (R2 > 0:99). Clip stiffness was 0.6 N/mm of extension arm tip displacement for minimal instrumentation artifact. A validation test was conducted through a comparison of strain clips, surface-mounted strain gauges and theoretical strain in an aluminium rod subjected to axial tensile loading. The two measurement techniques were used to determine the modulus of elasticity of the aluminium rod. Results were within 6% of the known modulus of elasticity for aluminium. A comparative biomechanical test was also performed on an equine third metacarpal specimen. The traditional bonded strain gauging method produced similar results as the new strain clip, but failed to measure ultimate strains since all strain gauges failed prior to specimen failure. Further investigations into the multiple uses of the clip are underway and recommendations for future versions of the clip are given. r 2003 Elsevier Science Ltd. All rights reserved. Keywords: Strain measurement; Bone; In vitro; Extensometer; Stress
1. Introduction Strain response of the skeletal system to external forces has been studied in a wide variety of applications (Roberts, 1966). This phenomenon has usually been measured using electrical-resistance strain gauges. Strain gauges have been implanted in vitro and in vivo on many different bone types and locations (Davies et al., 1993; Les et al., 1998; Schneider et al., 1981; Turner et al., 1975). Unfortunately, the use of gauges on bone has many associated problems. Successful strain gauging of a material is dependent on an intimate bonding interface. As bones are porous and saturated with fluid, preparing a surface for installation is difficult. Body fluids are also *Corresponding author. Tel.: +1-519-824-4120; fax: +1-519-8360227. E-mail address: [email protected] (R.J. Runciman).
extremely corrosive, and are able to permeate or destroy a wide variety of protective coatings on the gauge (Roberts, 1966), even in vitro. Other problems associated with strain gauges are their one-time, short-term use, and the fact that they cannot normally be used to specimen failure. For these reasons, some researchers have investigated alternatives for measuring bone deformation including instrumented staples and grip-mounted extensometers. Several limitations exist with these methods. First, instrumented staples can be damaged during insertion and the inherent rigidity of the staple will alter the stress and strain distribution in the bone. For grip-mounted extensometers, relative motion between bone and grips, cost and size are all drawbacks. This paper introduces a novel, multi-use, low-stiffness and low-cost transducer for in vitro strain measurements. The versatility of this design allows for the measuring of large strain deformations through to
0021-9290/03/$ - see front matter r 2003 Elsevier Science Ltd. All rights reserved. doi:10.1016/S0021-9290(03)00173-8
ARTICLE IN PRESS 1670
G. Whan et al. / Journal of Biomechanics 36 (2003) 1669–1674
Fig. 1. Schematic of exploded view of clip and photograph of clip mounted to aluminium rod during test. The strain clip composed of a ‘‘c’’ shaped stainless-steel clip, thickness of 1 mm, instrumented with four 350 O axial strain gauges (two bonded to the concave and two to the convex side of the end web) wired in a full Wheatstone bridge configuration. A pair of modular extension arms with knife edges have been added to facilitate the interaction with the test sample. The bottom arm acts as a potentiometer to allow for bridge balancing without the need for amplifier adjustments. A pair of rings with screws is used to mount the clip to the test sample, dimensions in mm.
specimen failure. This was accomplished through the design of a clip instrumented with strain gauges (hereby referred to as a strain clip) that utilises adjustable and replaceable arms, and for the application documented here, a pair of rings with screws serving as the bone/clip interface. This study explores the calibration and use of a modular strain clip in comparison to surface-mounted strain gauges and theoretical strain measurements on an aluminium bar. The strain clip was also assessed through its application to a section of in vitro bone under load.
2. Methods The clips were fabricated from stainless steel to the dimensions illustrated in Fig. 1. Two stainless-steel rings were designed to interface the test sample with the clips. The test sample was secured in the rings with two sharply pointed 6/40 stainless-steel screws. Adjustable steel extension arms were fabricated for the clips. The arms were shaped and attached to the clips with screws. One arm in each pair acted as a potentiometer by allowing the tip force to be adjusted, altering the stress and, therefore, the strain in the clip. This was used to make adjustments to the initial gauge reading without making amplifier adjustments and recalibrating. The tips of the extension arms were formed into knife edges to be snapped between threads of the adjacent screws.
During use, these knife edges articulated on the threaded portion of the screws. Four encapsulated 350 O axial strain gauges (MM CEA-06-250UN-350)1 were epoxy bonded in parallel to the inner and outer web of the strain clip following standard strain gauge application techniques (Vishay Measurement Group, 2001). Twenty-eight AWG PVC insulated lead wires were soldered to the gauges in a full Wheatstone bridge configuration. A protective coating of RTV silicone rubber was then applied to all four gauges. Clip calibration was accomplished using an adjustable height gauge fitted with threaded rods. Clip arms were placed between the height gauge and a second threaded rod mounted in a vise. Clip response was recorded for changes of 0.0254 mm (0.001 in) displacements determined by the height gauge (70.0127 mm). Bridge excitation and signal conditioning were accomplished using custom-built amplifiers (Analog Devices 2B30 modules) with an excitation voltage of 6 V and a gain of 10. Voltage output was recorded at 120 Hz using standard PC data acquisition software2 and a 16-bit A/D converter2. The voltage to displacement ratio for the clip was then determined using standard linear regression techniques.
1 2
Vishay Measurements Group, Raleigh, NC, USA. National Instruments, Austin, TX, USA.
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Fig. 2. Bone used in the comparative biomechanical test. The sample was removed from the mid-diaphysis of an equine third metacarpal and shaped from a pillar to the above shape. Two axial strain gauges were bonded to the surface on the front and back of the sample as shown and wired as independent 1/4 Wheatstone bridge circuits. The region of interest was shaped to be 20 mm long, 5 mm wide and 5 mm deep.
The stiffness of the clip was also tested. The upper arm of the clip was fixed in a vise. A series of weights were hung from the end of the lower arm, and the resultant tip deflection was measured using the height gauge. A clip stiffness factor was then calculated. To evaluate the performance of the clip relative to bonded strain gauges, a comparative test was performed using a long cylindrical aluminium rod of constant diameter (81 cm length; 1.27 cm diameter) strain gauged with two surface-mounted axial gauges (Showa N11FA-10-120-11) oriented 180 to each other. Two clips were placed between screws fixed onto each side of the rod using the rings (see Fig. 1). The screws were aligned and secured in the middle of the bar and perpendicular to the longitudinal axis of the rod. The gauges were attached to the same custom-built signal conditioning amplifiers completing the Wheatstone bridge configuration set to an excitation voltage of 6 V and a low gain. The aluminium rod was subjected to axial tension to a maximum of 4 kN at a load rate of 2 mm/min in a universal electromechanical testing machine (Instron model 4204) instrumented with a 50 kN load cell. Aluminium rod load, clip output and gauge output were all sampled at 120 Hz using the same data acquisition system. Clip results were converted to strains using the previously determined calibration factor. Strains measured with the surface-mounted gauges were determined using shunt calibration techniques and standard formulae (Dally and Riley, 1978). Strains from the two gauges and from the two clips were each averaged to find the strain at the centre of the rod and to eliminate the effect of any unwanted bending in the rod. Strains from the two techniques were then used to produce stress–strain curves and calculate the modulus of elasticity for aluminium.
A comparative biological test was conducted by applying the strain clip to samples of bone from the mid-dorsal diaphysis of equine third metacarpals. Samples were shaped into a two-dimensional hour glass profile (Fig. 2) using an air-driven router outfitted with a 1/4 in up spiral router bit. Backside shaping was also done, yielding a testing region with a constant cross sectional area of cortical bone (25 mm2). Samples were instrumented with axial gauges on the periosteal and the internal surfaces (see Fig. 2). The stainless-steel rings were placed over the samples before being positioned in two custom-built Instron aluminium grips. The rings were arranged with a nominal gauge length of 15 mm, the screws were tightened into the bone sample and the strain clips were placed or clipped into position on the screw threads. Samples were subjected to a tensile load at a rate of 6 mm/min to failure. The clip, gauge and load output voltages were collected as previously described. Clip and gauge outputs were each averaged to calculate the strain at the centre of the sample. Results from both techniques were used to determine the modulus of elasticity for the bone sample.
3. Results Calibration of clips exhibited a linear voltage response to displacements over a range of 30.5 mm (R2 > 0:99). With amplifier settings as documented above, the working range of the strain clips was 1.04 mm and the calibration factors for the two clips ranged from 0.40 to 0.45 V per 0.0254 mm (0.001 in) displacement. R2 values for the linear regression were above 0.99. A typical calibration graph can be seen in Fig. 3. Clip stiffness was 0.6 N/mm of displacement.
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Fig. 3. Typical calibration curve for the clips. Each point represents a tip displacement change of 0.0254 mm. Amplifier settings were 6 V excitation with a gain of 10. Clip output was linear over the entire region (R2 > 0:99).
Fig. 4. Typical validation test results on an aluminium rod fitted with surface-mounted strain gauges and the strain clips.
In the validation test conducted on the aluminium bar, a modulus of elasticity of 73 and 65 MPa were calculated using data from the bonded strain gauges and the clips, respectively. The modulus of elasticity for aluminium is quoted as 69 MPa (Baumeister, 1978), yielding an error of 6% or less for each method. Sample results from this test can be seen in Fig. 4. For the comparative biomechanical study, output data from the strain gauges adhered directly to the bone were compared to the strain clip results. Results from the two methods predicted a modulus of elasticity of bone within 1% of each other at low stresses, as shown in Fig. 5. Strain gauge failure occurred at 3000 mm, well before sample failure at approximately 9000 mm.
4. Discussion The demand for strain information has pushed researchers to investigate numerous strain measurement
Fig. 5. Typical results from the comparative test on a small bone sample. The surface-mounted strain gauge failed between 2500 and 3000 mm. Ultimate strain of the bone sample could not be found using the strain gauges. The strain clips continued to measure strain in the sample to failure, at approximately 9000 mm. There was a difference of 1% between the two methods at the point of gauge failure during the test.
techniques. The use of a pre-instrumented clip to measure strain would reduce many of the complexities associated with bone strain measurements made using surface-mounted gauges, instrumented staples or dedicated strain devices, especially for in vitro testing and testing ultimate material properties. The clips introduced in this paper offer many advantages over previously developed measurement techniques. Surface-mounted strain gauges when appropriate are very expensive. The strain clips introduced here incorporate only four strain gauges and have been repeatedly used with no deterioration in performance. The use of the rings and screws allows for total reusability of the clips, as well as the option of precutaneous placement of the screws, simplifying the instrumenting procedure. The rings allow a lowartifact strain measurement with minimum impact on the bone stress field. The clip shape and anchor interface have been chosen to reduce instrument stiffness and associated artifacts while optimising sensitivity. Other researchers have investigated alternatives to bonded strain gauges for measuring bone strain (Arndt et al., 1999; Butterman et al., 1994; Ekenman et al., 1998; Boyd et al., 2001; Reilly et al., 1974). Most of these devices have been titanium staple type units with pre-bonded gauges. The design of this clip improves on the use of the titanium staple by reducing the rigidity of the instrumented device and eliminating unwanted stress field artifacts. Clip stiffness was 0.6 N/mm of tip displacement. Calculated values for a titanium staple with an elastic modulus of 115 GPa reveals about 45,000 N of force generated per mm displacement of the staple leg. When this staple is inserted into a material
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such as bone with a significantly lower elastic modulus, load sharing will occur between the staple and the bone. This load sharing will alter the stress distribution in the bone, and therefore the strain being measured. The amount of load sharing would vary with not only the relative difference in elastic modulus’, but also bone hardness, interface design, bone thickness, and staple insertion depth. To overcome the effects of load sharing, the staples have typically been calibrated using a proportional factor to correct the strain measured using the staple to that of a surface-mounted gauge placed under the staple. This time-consuming step is unnecessary with the clip presented here and adds to the ease of use. The advantage of a linear relationship between strain and output of a strain measurement device cannot be overlooked. Output from the strain clip was linear over a large range and can therefore be used in a wide variety of applications. For strain measurements in the biological samples as discussed here, the equipment was adjusted to the application to achieve a high sensitivity for small changes in strain. In order to measure strain on a biological sample, this application incorporates a set of extension arms with a knife-edge interface between the screws of custom-built rings. A variety of extension arms could be designed and implemented for different applications. Using modified arms, clips can be adapted for tensile and compression testing, variations in sample size and interface methods. During the comparative biomechanical test, the prediction of the modulus of elasticity was hindered by failure of the bonded strain gauges. In one test the bonded strain gauge failed almost immediately and in all tests the gauges failed prior to sample destruction. This is not uncommon with surfacemounted gauges. This type of failure with strain gauges hinders their application measuring ultimate strains in samples. Estimates from the data that were collected before the strain gauges failed agreed with the modulus of elasticity found using the output from the strain clips. In vivo use of the strain clips is limited by the clip bone interface. Bone screws were initially investigated but artifacts resulting from the bone screws made the results unreliable. The pair of rings used in this paper were designed to reduce artifacts and allow for a strain reading by averaging the two clips for small sample in vitro testing. Our laboratory use of the strain clips has allowed us to identify a number of improvements that could be made to the current design. Repeated use indicated that bridge wiring was susceptible to damage. The use of a lighter gauge wire and strain relief would improve the durability of the strain clips. The strain clips could also be constructed with a bias to facilitate either tension or compression type testing. Pre-straining the clip before
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bonding the gauges, either in compression or tension would improve the working range of the clip. This would specialise the clips for either compression or tension applications.
5. Conclusions The introduction of a multi-use, low-cost strain measurement system that is simple to produce will be of particular interest to biomechanical laboratories. The strain clip is highly versatile in its modular design. The bone testing application included here is an example of just one of the many applications for the strain clips. Replaceable extension arms, high linearity over a working range of 30.5 mm, and simple calibration are all characteristics that will lead to the use of these clips in a variety of future applications.
Acknowledgements The authors would like to thank Sean Smith, Peter Perk, and Bill Verspagen from the School of Engineering for technical assistance; and NSERC and Sunlight Medical Ltd., Israel for funding this research.
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