Experimental set-up
An instrumented cylinder (diameter of 60 mm and a height of 100 mm) having dimensional characteristics similar to everyday-life objects such as a glass or a bottle was built to allow the opposition axis and force magnitude to be measured while it is manipulated. The external frame of the cylinder consists of two separate nylon 66 half-cylinders rigidly connected to a single 6-axis force/torque (F/T) sensor (ATI Industrial Automation, NC, USA, model Mini 40 SI-20-1 with a resolution in each channel:
FX,
FY = 1/100 N;
FZ = 1/50 N;
TX,
TY,
TZ = 1/4000 Nm). All forces and moments of force exerted by the fingers are measured through the transducer since the two half-cylinders are separated by a gap of 0.56 mm. One of the half-cylinders is press-fitted and locked with set screws on an adapter that was fixed on the sensitive side ("
tool side" as defined by ATI, see Figure
1C) of a single F/T sensor, enabling external forces and torques to be recorded (Figures
1A and
1C). The adapter consists of a machined hat-shaped nylon plate permitting adequate transfer of the forces and moments from the half-cylinders to the F/T sensor (Figures
1A and
1C, hatched area). The forces exerted on the non-sensitive half-cylinder are considered equal and opposite to the ones recorded on the opposite half-cylinder, assuming that stable manipulation of the instrumented cylinder is achieved.
| Figure 1Functioning of the instrumented cylinder and experimental set-up used for its calibration. The apparatus is designed to measure the orientation (θ) and vertical location (x) of the applied force (P) by either the index or thumb while exerting (more ...) |
In conjunction with the instrumented cylinder, a software program was developed (LabView v6.1, National Instruments, TX, USA) to record and process the 6-axis data from the F/T sensor. The software program provides a real-time display and recording of the experimental variables of interest, namely, opposition axis (θ), height (x) and resulting force (P) of the weight applied to the instrumented cylinder (Figure 1A). The center of pressure is expressed in terms of the angle and height of the force acting on the surface of the cylinder due to the applied loads (θ and x values in Figure 1A). All variables are obtained from computations based on the instrumented-cylinder characteristics (e.g. relative position of the F/T sensor, diameter) and measurements of the XYZ decomposed forces (F) and moments (M) captured from the F/T sensor embedded inside. The opposition axis was considered collinear through the cylinder's central axis. The program used the following equations to compute the variables of interest in a cylindrical coordinates referential (r, θ, and x, where r is fixed here to the radius of the cylinder and x0 is the position of the center of the F/T sensor relative to the top of the cylinder).
Calibration
The instrumented cylinder was calibrated using precision devices including an angular positioning tool (milling table) and a linear positioning plate (Figure
1C). The cylinder was firmly clipped horizontally on the angular positioning tool in order to be able to rotate it and to measure the weights vertically applied to its surface. The angular positioning tool had a vernier, giving a measurement precision of 0.1°, while the positioning plate comprised circular, center-spaced holes of 1 cm in which the weight support could be inserted. The weight support had a pointed tip allowing the standard weights to be placed precisely (combination of angle and height) on the surface of the cylinder. Also, the weight of this support was subtracted from the load measured by the cylinder, since a baseline was established before recording began, while the weight support was in contact with the surface. With the instrumented cylinder weighing approximately 100 g, the range of weights used for the calibration was dictated by the most probable forces exerted by a subject manipulating the object. Multiple combinations of standard weights (100, 200, 300, 400 and 500 g) and positions (angles ranging from -80° to 80° in increments of 20°, with 0° being aligned with the center of the force cell flat surfaces; height ranging from 10 to 90 mm in increments of 10 mm from the top of the cylinder; see Figures
1A and
1C) were used for the purpose of calibration (5 weights × 9 angles × 9 heights = 405 combinations). The opposition axis (
θ), height of precision grip (
x) and resulting force (
P) were averaged for each combination from 500 data points acquired during a 5-s acquisition period at 100 Hz.
Empirical data processing for calibration
A descriptive statistical analysis including computation of means, standard deviations (SD), confidence intervals at 95% (CI) and absolute error (AE) of each
P value obtained was performed on the calibration data recorded when applying a given weight to the cylinder at the different locations (
x and
θ). For the center of pressure (COP) variables (
θ,
x), the mean, SD, CI and AE values were computed by averaging data for the different weights applied to the cylinder for each combination of
θ and
x (matrix of 9 × 9, see Figure
1C).
The weights used to determine the amplitude of P were precise (1000 g × 10 g Brass Hook Weight Set, item# 46206-00, Ohaus, USA) and were used as gold standards. In contrast, the experimental set-up had its own sources of error regarding the location of the applied force, as will be addressed later in the discussion. Thus, for the COP variables, the theoretical values of θ or x chosen in the spatial referential determined by the experimental set-up (see Figure 1C) were considered as absolute while their averaged values over all the weights and for all θ or x (depending on the variable of interest) were used to obtain gold standards. Before obtaining gold standards, we intended to minimize the difference between all points from the absolute referential and the averaged values computed for all θ or all x in order to detect a possible systematic error introduced in the measurements by the experimental set-up. The AEs difference between expected theoretical value and averaged empirical value) on the COP variables indicated a tendency in the measurements to systematically over- or undershoot the expected measures. Concretely, the measurements for the angles tested were averaged for all weights and heights tested at a single angle and vice-versa for the heights tested. This procedure revealed a systematic offset of about 1.5° and 0.5 mm between the theoretical referential and the computed means of angle and height measurements, respectively. This offset was always over (heights) or under (angles) the expected values, representing a systematic error in the empirical data that we subtracted from all the empirical measurements, i.e. before obtaining the COP gold standards. The AEs on the COP variables were then computed as the difference between the mean of the variable of interest over all the weights at a specific point (θ, x) and the gold standards (both corrected for systematic offset), while the AEs on weights were simply the difference between the measured and standard weights used during calibration.
For P statistics, the use of standard weights (gold standards) allowed us to compare each measurement with a specific weight (9 heights × 9 orientations = 81 combinations) to the real weight applied. On the other hand, to determine the spatial precision and accuracy of the instrumented cylinder measurements, we relied on means, SDs and CIs given by the frequency distribution of the COP variables. Means and SDs allowed us to verify that the distributions of COP variables were centered near the expected values (based on the calibration set-up referential) and presented a narrow deviation from the average, which produced a high precision and accuracy. CIs gave us another way of visualizing the precision of the instrument, since 95% of the measurements performed lie within the range of the CI.
Variations of pinch force using different orientations
Six subjects (two men and four women aged between 21 and 45 years old) participated in the study. This experiment was approved by the research ethics committee of our institution and all participants gave their informed consent before the study began. All subjects were right-handed, as evaluated using the 'Edinburgh Handedness Inventory' (Oldfield, 1971). The subject sat on a chair without armrests facing the instrumented cylinder placed at his/her midline on a table. His/her trunk was located 15 cm from the edge of the table, 32.5 cm from the cylinder, which was placed on the table (Figure
2). The subject's hands were placed on the table, 12 cm each side of the midline. At the request of the experimenter, the subject was asked to reach, pinch and lift the cylinder at his/her own pace with the right thumb and index finger pads to a height of approximately 10 cm and maintain this position for 10 s (Figures
1B and
2). The finger pads had to be aligned with one pair of colour markers (red: 45°, green: 22° and yellow: -22°) visible on the top of the instrument and indicating the approximate opposition axis required. Only visual inspection by the experimenter was used to determine whether subjects had used the opposition axis required and the exact opposition axis was calculated using the instrumented cylinder. It is important to note that the reference axis for the angle measurements is the
Z axis of the transducer, as shown in Figure
1A. Therefore, each marker pair was positioned on the top extremities at clockwise angles relative to the subject's medial line (see Figure
2). Ten trials were performed for each of the three different orientations (45°, 22° and -22°). The wrist joint amplitude was measured with an electro-goniometer (model SG65, Biometrics Ltd., UK). Each condition was evaluated 10 times and the order was randomly administered for each subject. The amplitude of the force applied by the finger pads (
P), their opposition axis (
θ) and their height (
x) relative to the top of the cylinder were given by the instrumented cylinder. The movement was divided into two main phases: a dynamic phase, when the object is lifted from the table, and a static phase, when the object is stabilized in the air before being deposited on the table. These two phases were chosen because the grip forces observed during the dynamic phase were noticeably different from those measured during the static phase due to the inertial forces caused by acceleration and deceleration of the object and the following adaptation of grip force while maintaining the object in the air [
10,
12]. The beginning of the dynamic phase corresponded with the onset of the GF and was determined as the first point exceeding 2 SD from the mean baseline of GF and having a positive derivative of GF (
dGF) for at least six consecutive points. The end of the dynamic phase was temporally defined as 1450 ms after the first minimal amplitude of
dGF following the maximal amplitude of GF. This period of 1450 ms was arbitrarily chosen after visualizing numerous empirical signals. We analyzed the data for two selected periods of 250 ms measured respectively while the subject lifted the object in the air (maximal amplitude of the dynamic period) and about 5 s after the subject had been holding the object in the air (middle of the static period). The pinch force value and the parameters of the axis of opposition were then averaged in these two windows.
| Figure 2Experimental set-up for testing grasps orientations. A subject is required to execute successive series of lifts of the instrumented cylinder to a height of approximately 10 cm using his right hand with the finger pads aligned at different orientations (more ...) |