# Search Results

### Vladimir M. Zatsiorsky

A rather messy situation exists in the motor control literature with the notion of muscle and joint viscosity. The source of the confusion lies in attempts to study human movement using a simple mechanical concept that was proposed for uncomplicated objects such as a gel or gas. Although A.V. Hill (1938) wrote, “The 'viscosity' hypothesis must be dismissed” (p. 193), the concept of muscle/joint viscosity is still very popular in the literature. Distressingly, the reported values of muscle/joint viscosity differ greatly. Eleven dissimilar “viscosities” are briefly discussed. They represent disparate characteristics of the human motion system. It seems that the concept of viscosity is inadequate for describing motor control phenomena.

### Vladimir M. Zatsiorsky and Marcos Duarte

The goal of this study was to explore the rambling-trembling decomposition in quiet standing. The center of pressure (COP) and the horizontal ground reaction force (F_{hor}) were registered in healthy subjects standing in an upright bipedal posture on a force platform. The COP positions at the instants when F_{hor} = 0 were identified *(instant equilibrium points*, IEP) for the anterior-posterior direction, then the COP time series, were partitioned into its components using 2 different techniques, *rambling-trembling decomposition* and *gravity line decomposition*. The two decomposition techniques provided very similar results. An unexpectedly large correlation between the trembling trajectory and the difference between COP and gravity line was found, *r* = 0.91 (range, 0.83 < *r* < 0.98). The correlation implies that the GL moves from an IEP to the subsequent IEP along a smooth trajectory that can be predicted by the spline approximation. A substantial negative cross-correlation at a zero time lag was observed between the trembling and the F_{hor}, -0.90 < *r* < -0.75. For the rambling trajectory, the coefficients of correlation with F_{hor} were low, -0.33 < *r* < -0.05. The data support the hypothesis that during quiet standing the body sways for two reasons: the migration of the reference point (rambling) and the deviation away from that point (trembling).

### Vladimir M. Zatsiorsky and Nikolai Yakunin

Despite relatively numerous studies, the biomechanics of rowing remains poorly understood. Much of the data is contradictory and, worse still, there appears to be a lack of consensus on the mechanical background of rowing, which leads to different approaches to the measurement of a number of parameters known by the same terms. This makes direct comparison impossible. For this reason, the present review divides the discussion of relevant biomechanical problems into two stages. The first stage involves the construction of mechanical models of the rowing element under consideration, compilation of equations, and determination of parameters used in these equations. In the second stage, experimentally obtained empirical data on these parameters are discussed.

### Vladimir M. Zatsiorsky and Marcos Duarte

A method of decomposing stabilograms into two components, termed rambling and trembling, was developed. The rambling component reveals the motion of a moving reference point with respect to which the body's equilibrium is instantantly maintained. The trembling component reflects body oscillation around the reference point trajectory. The concepts of instant equilibrium point (IEP) and discrete IEP trajectory are introduced. The rambling trajectory was computed by interpolating the discrete IEP trajectory with cubic spline functions. The trembling trajectory is found as a difference between the approximated rambling trajectory and the COP trajectory. Instant values of the trembling trajectory are negatively correlated with the values of the horizontal ground reaction force at a zero time lag. It suggests that trembling is strongly influenced by a restoring force proportional to the magnitude of COP deviation from the rambling trajectory and acts without a time delay. An increment in relative COP position per unit of the restoring force, in mm/N, was on average 1.4 ± 0.4. The contribution of rambling and trembling components in the stabilogram was ascertained. The rambling variability is approximately three times larger than the trembling variability.

### Michael M. Morlock and Vladimir M. Zatsiorsky

The performance in bobsledding is influenced by several factors. This study concentrated on influences of the environment and the bobsled crew on the final time of a bobsled run. The analysis was performed with data collected during the four-man competition at the 1988 Winter Olympic Games in Calgary. It was shown that the start order, the ice temperature, and the push time together explain about 50% of the variance in the performance (α=0.05). It is suggested that the existing rule concerning the start order in a heat be modified to guarantee a fair competition. Selected speed and turn time variables were shown to give an indication of the characteristics and the important sections of the bobsled track at Canada Olympic Park. It is speculated that the optimization of turn times is more important than the increase in speed in a turn.

### Mark L. Latash, Fan Gao and Vladimir M. Zatsiorsky

The method of multidimensional scaling was applied to matrices of finger interaction (IFM) computed for individual participants for finger force production tasks. When IFMs for young controls, elderly, and persons with Down syndrome were pooled, only two dimensions described interpersonal differences; these were related to total force and to the total amount of enslaving. When IFMs for each group were analyzed separately, subpopulation-specific dimensions were found. Potentially, this analysis can be applied to discover meaningful dimensions that reflect differences in indices of finger interaction across and within subpopulations which differ in their apparent ability to use the hand. It may also be useful for tracking changes in finger interaction that occur in the process of specialized training or motor rehabilitation.

### Koichiro Kanatani-Fujimoto, Betty V. Lazareva and Vladimir M. Zatsiorsky

A method for analysis of time-series data, *local proportional scaling* (LPS), is proposed and its applications in motor control and biomechanics are discussed. The method is based on comparison of two time curves: a reference curve x(t) and a test curve x'(t'). By assumption, x'(t') is received from x(t) by local affine transformations, local extensions/compressions along the x and t axes [x(t)→x'(t'), where → stands for the local extensions/compressions along the x and t axes]. The aim of the LPS method is to discover the underlying transformations, including *gain indexes, time epochs, velocity quotients, time segments,* and *time quotients.* The LPS method can be used for (a) comparing the time-series curves in a concise transparent manner; (b) scaling the curves, bringing x'(t') in conformity with x(t); (c) automatic segmentation of the time series data; and (d) data classification.

### Gregory P. Slota, Mark L. Latash and Vladimir M. Zatsiorsky

When grasping and manipulating objects, the central controller utilizes the mechanical advantage of the normal forces of the fingers for torque production. Whether the same is valid for tangential forces is unknown. The main purpose of this study was to determine the patterns of finger tangential forces and the use of mechanical advantage as a control mechanism when dealing with objects of nonuniform finger positioning. A complementary goal was to explore the interaction of mechanical advantage (moment arm) and the role a finger has as a torque agonist/antagonist with respect to external torques (±0.4 N m). Five 6-*df* force/torque transducers measured finger forces while subjects held a prism handle (6 cm width × 9 cm height) with and without a single finger displaced 2 cm (handle width). The effect of increasing the tangential moment arm was significant (*p* < .01) for increasing tangential forces (in >70% of trials) and hence creating greater moments. Thus, the data provides evidence that the grasping system as a rule utilizes mechanical advantage for generating tangential forces. The increase in tangential force was independent of whether the finger was acting as a torque agonist or antagonist, revealing their effects to be additive.

### Adriana V. Savescu, Mark L. Latash and Vladimir M. Zatsiorsky

This article proposes a technique to calculate the coefficient of friction for the fingertip– object interface. Twelve subjects (6 males and 6 females) participated in two experiments. During the first experiment (the imposed displacement method), a 3-D force sensor was moved horizontally while the subjects applied a specified normal force (4 N, 8 N, 12 N) on the surface of a sensor covered with different materials (sandpaper, cotton, rayon, polyester, and silk).The *normal force* and the *tangential force* (i.e., the force due to the sensor motion) were recorded. The *coefficient of friction* (µ_{d}) was calculated as the ratio between the tangential force and the normal force. In the second experiment (the beginning slip method), a small instrumented object was gripped between the index finger and the thumb, held stationary in the air, and then allowed to drop. The weight (200 g, 500 g, and 1,000 g) and the surface (sandpaper, cotton, rayon, polyester, and silk) in contact with the digits varied across trials. The same sensor as in the first experiment was used to record the *normal force* (in a horizontal direction) and the *tangential force* (in the vertical direction). The *slip force* (i.e., the minimal normal force or grip force necessary to prevent slipping) was estimated as the force at the moment when the object just began to slip. The coefficient of friction was calculated as the ratio between the tangential force and the slip force. The results show that (1) the imposed displacement method is reliable; (2) except sandpaper, for all other materials the coefficient of friction did not depend on the normal force; (3) the *skin–sandpaper* coefficient of friction was the highest µ_{d} = 0.96 ± 0.09 (for 4-N normal force) and the *skin–rayon* rayon coefficient of friction was the smallest µ_{d} = 0.36 ± 0.10; (4) no significant difference between the coefficients of friction determined with the imposed displacement method and the beginning slip method was observed. We view the imposed displacement technique as having an advantage as compared with the beginning slip method, which is more cumbersome (e.g., dropped object should be protected from impacts) and prone to subjective errors owing to the uncertainty in determining the instance of the slip initiation (i.e., impeding sliding).