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Zong-Ming Li

Mechanical degrees of freedom (DOF) are defined as the minimum number of independent coordinates needed to describe a system’s position. The human musculoskeletal system has many mechanical DOF through which countless movements are accomplished. In the motor control field, one of the aspirations is to understand how the many DOF are organized for movement execution—the so-called DOF problem. Natural movements are characterized by the coordination of the DOF such that few vary independently. The concept of functional degrees of freedom (fDOF) is introduced to describe the very limited DOF of purposeful, coordinated movements. Deterministic (i.e., constraint satisfaction) and statistical (i.e., principal component analysis) approaches are used to determine fDOF. In contrast to DOF as a mechanical descriptor, fDOF emphasizes the mechanisms of human movements and corroborates our search for the solution to the DOF problem.

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Anderson Nascimento Guimarães, Herbert Ugrinowitsch, Juliana Bayeux Dascal, Alessandra Beggiato Porto, and Victor Hugo Alves Okazaki

(bones, joints, muscles, etc.), which have countless combination possibilities, can be controlled by a single effector system (central nervous system). For Bernstein ( 1967 ), the solution to this problem would be mastery over the degrees of freedom (DF), known as the independent components of the

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Anderson Nascimento Guimarães, Herbert Ugrinowitsch, Juliana Bayeux Dascal, and Victor Hugo Alves Okazaki

coordinate movements and generate specific motor responses ( Turvey, 1990 ). This situation, which demonstrates the complexity of coordinated motor skills control, has been known as the degrees of freedom (DF) problem ( Bernstein, 1967 ). The DF represent an infinite number of different ways and combinations

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Mark L. Latash

redundancy as the central problem of motor control. He wrote that the central problem of motor control is in the elimination of redundant degrees of freedom ( Bernstein, 1967 ). Similar problems emerge for other tasks and at other levels of analysis—for example, how does the CNS define muscle forces and

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Dennis Wootten and Maury L. Hull

Described is the design of a foot/pedal interface intended as a research tool in the study of overuse knee injuries in cycling. The interface enables the systematic variation of factors that may affect loads transmitted by the knee joint. It permits two degrees of freedom of movement, inversion/eversion and abduction/adduction rotations, either separately or in combination. The movement permitted by each degree of freedom can be either free or resisted by spring assemblies. Sample data were collected to demonstrate the function of the foot/pedal interface. With no spring resistance, the interface functioned as intended by allowing free movement of the foot. Significant interaction was seen between the two degrees of freedom, with more motion and a larger absolute mean occurring when both degrees of freedom were allowed simultaneously. This emphasizes the need for a multi-degree-of-freedom interface when undertaking a comprehensive study of the factors affecting loads transmitted by the knee.

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Karl M. Newell and Steven Morrison

This paper presents a framework for an evolving dynamical landscape of movement forms and their stability over the lifespan. It is proposed that the complexity and dimensionality of movement forms can expand and contract on a number of growth/decay time scales of change including those of adaptation, development, and learning. The expansion and contraction is reflected in: (1) the range of potential movement forms of the individual in developmental time; and (2) the dimensionality and complexity of any single movement form at a moment of observation given the confluence of individual, environmental, and task constraints. It is postulated that practice, exercise, and fatigue also coalesce to change the time scales of complexity and dimension of movement forms.

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Gregor Schöner and John P. Scholz

An important aspect of the study of multi-degree-of-freedom motor control is the analysis of high-dimensional variance data. Through the “uncontrolled manifold” (UCM) approach the structure in such data can be discovered and interpreted. The covariation by randomization (CR) approach provides nonlinear and potentially multi-dimensional measures of covariance. We critically examine these two approaches and compare them relative to the three fundamental issues of choice of variables, choice of model, and adoption of either a geometrical or a correlational view of variance. The UCM approach is a geometrical approach that seeks to discover the structure of variance in multi-degree-of-freedom task spaces in which all degrees of freedom have a common metric. The structure of variance in that space is interpreted in terms of its meaning for task variables. The CR approach seeks to uncover correlations between interpretable elemental variables. It requires a defined and common metric in the space of task variables, but not the elemental variables. Although the CR approach is better suited for systems with strong nonlinearities, variance structure that is not caused by correlation but by different amounts of variance in the different elemental variables is undetected by this approach.

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Steven Rowson, Jonathan G. Beckwith, Jeffrey J. Chu, Daniel S. Leonard, Richard M. Greenwald, and Stefan M. Duma

The high incidence rate of concussions in football provides a unique opportunity to collect biomechanical data to characterize mild traumatic brain injury. The goal of this study was to validate a six degree of freedom (6DOF) measurement device with 12 single-axis accelerometers that uses a novel algorithm to compute linear and angular head accelerations for each axis of the head. The 6DOF device can be integrated into existing football helmets and is capable of wireless data transmission. A football helmet equipped with the 6DOF device was fitted to a Hybrid III head instrumented with a 9 accelerometer array. The helmet was impacted using a pneumatic linear impactor. Hybrid III head accelerations were compared with that of the 6DOF device. For all impacts, peak Hybrid III head accelerations ranged from 24 g to 176 g and 1,506 rad/s2 to 14,431 rad/s2. Average errors for peak linear and angular head acceleration were 1% ± 18% and 3% ± 24%, respectively. The average RMS error of the temporal response for each impact was 12.5 g and 907 rad/s2.

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Gertjan J.C. Ettema, Emma Taylor, J. David North, and Vaughan Kippers

This study’s aim was to identify the effect of oscillation of torques in isometric tasks under identical mechanical conditions on the muscle synergies used. It was hypothesized that bi-functional muscles would play a lesser role in torque oscillation, because they would also generate an undesired oscillation. Thus, changes in muscle synergies were expected as a consequence of oscillation in torque generation. The effect of the trajectory of torque generation was investigated in dual-degrees-of-freedom submaximal isometric oscillation torque tasks at the elbow. The torques were flexion-extension and supination-pronation. Oscillation torques were compared with static torque generations at four torque positions during oscillation. Muscle activity was determined with surface electromyography. Compared with the static torque tasks, the oscillation tasks showed an overall increased muscle activity. The oscillation tasks, however, showed similar activity patterns and muscle synergies compared to the static composite tasks. It was found that the motor system is well able to control different orthogonal combinations of slow torque oscillations and constant torques by employing a single oscillating muscle synergy.

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Cameron T. Gibbons, Polemnia G. Amazeen, and Aaron D. Likens

; Latash & Turvey, 1996 ). Bernstein’s degrees of freedom problem refers to the impossibility of specifying positional and kinematic information for the control of each of those degrees of freedom in the service of a particular movement goal. Bernstein’s solution was to reduce the degrees of freedom by the