Measuring the ground reaction forces of a single leg is indispensable to understanding the dynamics of legged locomotion. Because of the technical state of the art, investigations are limited to animals with a body mass above 1 g. Here we present the design, fabrication, calibration and performance of a novel ultra-miniature force platform at the micronewton level. The sensor was built using the stereolithography technology and is equipped with semiconductor strain gauges. We found a highly linear signal response in the calibrated force range to ±1300 μN. Individual tests revealed that our force plate still shows a linear response at forces as great as 4 mN, confirming a large measuring range and particular robustness. The sensitivity was above 50 V N−1 in all directions, which makes it possible to resolve forces of 10 μN. We demonstrated the suitability of the device on the basis of a typical ground reaction force measurement of an ant, Formica polyctena.
Ground reaction forces represent the ‘footprint’ of the dynamics of legged locomotion. Depending on the force range and the object of investigation, a number of measurement techniques are available (Table 1). Each of these is based on deformations of measuring instruments when a force is applied. Accordingly, in most cases, cantilevers equipped with strain gauges or piezo elements are used as sensing units. In the range from 1 mN up to 30 kN, three-dimensional (3D) force plates are commercially available from different manufacturers. However, for a variety of reasons, many force sensors used in biomechanical studies on small animals are custom-made. Over the last few decades, several researchers have developed two-dimensional miniature force plates for species weighing only a few grams (Heglund, 1981; Full and Tu, 1990; Drechsler and Federle, 2006; Wood et al., 2009; Lin and Trimmer, 2012). Versions of the Heglund (Heglund, 1981) force plate design were most often used to design measuring instruments for animals of different size. Furthermore, it was possible to build 3D force plates via the advancement of this design (Full et al., 1991; Katz and Gosline, 1993; Autumn et al., 2006; Dai et al., 2011). Another approach consisting of bronze springs with attached strain gauges led to a force plate within the same sensitivity range (Blickhan and Barth, 1985). Unfortunately, none of these devices are suitable to resolve 3D forces at the micronewton level. They are therefore not able to capture the dynamics of small insects, for example, in the size range of an ant.
In this area, ultrasensitive, silicon-based microelectromechanical systems (MEMS) devices seem to be the method of choice. Various prototypes and their principal usability in the field of insect biomechanics have already been demonstrated (Bartsch et al., 2007; Muntwyler et al., 2010; Kan et al., 2013). However, a major problem with these sensors is their high fragility and the associated small measuring range. Muntwyler and colleagues reported a force range for their device from ±20 to ±200 μN (Muntwyler et al., 2010). Ants are able to generate forces up to a multiple of their own weight with their mandibles. Measurements have been published showing that ants of the species Cataglyphis fortis could easily carry loads of 40 mg (Zollikofer, 1994). It is to be expected that these animals may generate much higher forces with their mandibles and legs, which would damage the MEMS devices.
In a first attempt, we have succeeded in building a 3D miniature force plate based on PVC springs as well as measuring ground reaction forces in ants (Reinhardt et al., 2009). This sensor combined an adequate sensitivity and robustness for our task. However, this design variant, consisting of a horizontal bar cross-connected with two orthogonally oriented bars, caused undesirable crosstalk effects. In this paper, we present a detailed description of a further development of our first prototype with significantly lower crosstalk between the channels.
Dependence on site of force application
One example of a static calibration experiment including force calculation under application of all corrective calculations is shown in Fig. 2.
In Fig. 4, we present one example of a dynamic experiment including force calculation under application of all corrective calculations.
Natural frequencies of the three force directions were calculated to be between 200 and 380 Hz (see Table 3). We conducted an experiment to determine the actual eigenfrequencies of the prototype. This was done by repeatedly tapping on the weighing table with approximately 5 Hz over a period of 60 s. As can be seen from Fig. 5, all significant oscillations were above 200 Hz.
Ground reaction forces in ants
One possible field of application of our miniature force plate is in research on small insects. The device has already been successfully deployed within an experimental setup for biomechanical analysis of ant locomotion. During 6 months of operation, in total approximately 1500 runs have been registered, implicating at least 3000 runs in which the platform survived without damage or decreased performance. One exemplary measurement of the red wood ant Formica polyctena is shown in Fig. 6.
In this work, we present a new design and fabrication method of a triaxial miniature force plate for the micronewton range. A 3D beam construction was built using the highly precise stereolithography (SLA) technique. The prototype was equipped with commercially available semiconductor strain gauges and connected to a digital multi-channel amplifier system. We here demonstrate that the properties of the used material are suitable for sensor design. The polycarbonate similar material is light, very elastic, well damped, and the adhesive bond with the strain gauges is solid and permanent. For the investigated range up to 1.3 mN, we found a highly linear behaviour in all directions. Furthermore, individual experiments with loads of up to 4 mN proved the same characteristics and confirmed the particular robustness of our force plate. This property in particular is a distinct advantage compared with other highly sensitive MEMS devices described in the literature (Bartsch et al., 2007; Muntwyler et al., 2010; Kan et al., 2013). These sensors are extremely fragile and are not able to resist the maximum forces that, for instance, ants can produce with their mandibles. Thus, MEMS devices are, despite their high sensitivities, rather unsuitable for experiments with freely running insects. Additionally, they are considerably more expensive to produce. The stereolithographic manufacturing processes offer freedom of design, which makes it possible to adapt the sensor to a wide range of applications. Therefore, our measuring device can be applied far beyond the field of insect biomechanics. For example, the force plate could be invaluable to the design and testing of the next generation of micro-robots (Hoffman and Wood, 2011; Ozcan et al., 2013).
Although in the planning phase we went to great lengths to reach low crosstalk between the individual force components, the crosstalk effect was still present. The crosstalk from the x- to the y-direction could most probably be avoided by simply positioning the strain gauge Sy higher. Although the current arrangement ensures maximum sensitivity, it also causes a relatively high transverse strain in the piezoresistor during loads in the x-direction. Fig. 7A shows that the lower half of Sy is placed on a stable base while the upper half is attached to the considerably more flexible beam. With the current design, eccentric vertical loads will always result in crosstalk effects. We minimize this effect by indicating the point of force application as precisely as possible so that corrective calculations can be performed subsequently. When the sensor is used, as in our case, for single leg ground reaction force measurements of small insects, this point is recorded anyway from kinematics. Another possibility is to decrease the size of the plate; however, this reduces the probability that the animals hit the plate with one leg while running. The standard method to use force distribution between four vertical channels to calculate or to compensate for the site of force application yielded unreproducible nonlinear behaviour of the vertical component. Certainly, design space is limited by size (strain gauges), mass (natural frequency) and sensitivity. Through the chosen L-shaped design, the mentioned nonlinearities are avoided and it is easily possible to arrange an array of up to four plates. This may allow us in future to measure ground reaction forces of the legs of one tripod synchronously.
MATERIALS AND METHODS
Design and fabrication of the force plate
We used 3D CAD and simulation software SolidWorks 2010 (Waltham, MA, USA) to design the miniature force plate and to calculate its properties using the finite element method (FEM). The vertical (z) component of the sensor is composed of a parallel stack of two cantilever beam springs aligned horizontally and perpendicular to each other in a L shape (Fig. 7A). At their free ends, the springs are connected by a rigid vertical element. Perpendicularly, two additional bar springs are mounted – oriented orthogonal to each other – allowing us to register forces in the plane of movement (x, y). At the end of the upper beam, a square tread is attached. Via this element, forces can be introduced. The arrangement of two orthogonally oriented spring blade elements represents a commonly used design for two-dimensional sensors (Heglund, 1981; Klärner and Barnes, 1986; Drechsler and Federle, 2006). It ensures low crosstalk effects, is easy to manufacture and its properties are predictable by beam theory. Thus, the sensor can be adapted in advance to its later application. Our design has the advantage that the horizontal beam construction (z) is insensitive to loads in the x- and y-directions. Consequently, low crosstalk effects are to be expected and have been predicted by FEM (Fig. 8).
The natural frequencies were predicted to be between 200 and 380 Hz (Table 3). For fabrication, the 3D CAD model was transferred into STL format and the prototype was built layer-by-layer via SLA. In particular, the Viper si2 SLA system (3D Systems, Darmstadt, Germany) was used with a layer thickness of 0.05 mm and a material very similar to polycarbonate (Accura 60, 3D Systems, Darmstadt, Germany). At the points of the largest strain (red rectangles, Fig. 7A), each dimension was equipped with one semiconductor strain gauge of type KSP-3-120-F2-11 (Kyowa, Tokyo, Japan). For their application, a cyano-acrylate based adhesive from the same manufacturer was used (CC-33A).
The sensitive unit was installed in a computer numerical control (CNC)-fabricated aluminium housing and wired with a shielded low-noise cable. We used the MGCplus data acquisition system (Hottinger Baldwin Messtechnik, Darmstadt, Germany) for signal processing. The amplifier module ML10B with an AP01i connection board was used to integrate the semiconductor strain gauges into a Wheatstone bridge circuit with a 1 V bridge excitation. No filter was chosen and the nominal value was set to 1 mV V−1 for maximum gain. A desktop PC with the data acquisition software Catman Easy V3.3.3 (Hottinger Baldwin Messtechnik, Darmstadt, Germany) was connected through a USB communication processor (CP22). Raw data were saved in MDF format and all further steps of data processing were made in MATLAB R2010a (The MathWorks, Natick, MA, USA). A Fastcam SA3 high-speed video system (Photron, San Diego, CA, USA) was integrated in the setup to capture kinematics. We mounted the sensor to a vibration isolation workstation (MK2601, Minus K Technology, Inglewood, CA, USA) with a natural frequency below 1 Hz.
Our simulations and calibration experiments have shown that the measurement of the force in the z-direction is independent from the point of force application. However, the upright-standing beams also bend at off-centre vertical loads (see Fig. 2D). To quantify this effect, we repeated the calibration process in the z-direction at nine different positions. We used scale paper bonded to the tread to define these points. They were arranged in a 3×3 matrix with a grid width of 1 mm around the centre. An example of an off-centre calibration is illustrated in Fig. 2.
Besides the static calibration, we performed dynamic experiments using a steel ball with a mass of 32.8 mg and a diameter of 2 mm. For this, the force plate was tilted by an angle of approximately 2 deg to the plane and the steel ball was allowed to roll across the plate with a starting distance of approximately 4 cm. Because of the marginal inclination, it was assumed that only a vertical force of 322 μN acted on the sensor, when the steel ball was on the plate. The slope was chosen so that the ball rolled closely along the horizontal axes of the coordinate system (see Fig. 3A). We repeated this procedure 13 times for the x- and y-directions. The signals of the force sensor were recorded synchronously with high-speed videos at 1200 Hz (resolution: 0.077 mm pixel−1). Steel ball kinematics were digitized using the software WINanalyze 3D (Version 2.1.1, Mikromak, Berlin, Germany). On average, the ball rolled across the plate with a velocity of 7.1±1.1 cm s−1 (mean ± s.d.) and the contact duration was 57.2±8.6 ms. Thus, in every single experiment, ~70 data points were registered to map the complete plate length of 4 mm. These data points were used to re-calculate the calibration factor in the z-direction and the crosstalk effect on Sx and Sy at off-centre vertical (z) loads.
This work was funded by the German Research Foundation (DFG) [BL 236/20-1 to R.B.].
The authors declare no competing financial interests.