As humans move through their environment, they must change the stiffness of their joints in order to effectively interact with their surroundings. Stiffness is the degree to a which an object resists deformation when subjected to a known force. This idea is also referred to as impedance, however, sometimes the idea of deformation under a given load is discussed under the term "compliance" which is the opposite of stiffness (defined as the amount an object deforms under a certain known load). In order to effectively interact with their environment, humans must adjust the stiffness of their limbs. This is accomplished via the co-contraction of antagonistic muscle groups. Humans use neural control along with the mechanical constraints of the body to adjust this stiffness as the body performs various tasks. It has been shown that humans change the stiffness of their limbs as they perform tasks such as hopping, performing accurate reaching tasks, or running on different surfaces. While the exact method by which this neural-modulation of limb stiffness occurs is unknown, many different hypotheses have been proposed. A thorough understanding of how and why the brain controls limb stiffness could lead to improvements in many robotic technologies that attempt to mimic human movement.
Stiffness Stiffness is typically viewed as a material property describing the amount a material deforms under a given force as described by Hooke's law. This means that objects with higher stiffness are more difficult to bend or deform than objects with lower stiffnesses. This concept can be extended to the limbs and joints of biological organisms in which stiffness describes the degree to which a limb or joint deflects (or bends) under a given load. Limb stiffness can also be described as the static component of impedance. Humans change the stiffness of their limbs and joints to adapt to their environment. Limb and joint stiffness has been previously studied and can be quantified in various ways. The basic principle for calculating stiffness is dividing the deformation of a limb by the force applied to the limb, however, there are multiple methods of quantifying limb and joint stiffness with various pros and cons. When quantifying limb stiffness, one cannot simply sum the individual joint stiffnesses due to the nonlinearities of the multi-joint system. A few of the specific methods for calculating limb stiffness can be seen below: Vertical Stiffness (k vert) is a quantitative measure of leg stiffness that can be defined by the equations below:
K vert = F max Δ y {\displaystyle K_{\text{vert}}={\frac {F_{\text{max}}}{\Delta y}}}
Where F max is the maximum vertical force and delta y is the maximum vertical displacement of the center of mass
K vert = m ( 2 π P ) 2 {\displaystyle K_{\text{vert}}=m({\frac {2\pi }{P}})^{2}}
Where m is the body mass and P is the period of vertical vibration
K vert = m ω 0 2 {\displaystyle K_{\text{vert}}=m\omega _{\text{0}}^{2}}
Where m is the mass of the body mass and ω 0 is the natural frequency of oscillation Limb Stiffness (K_limb) is the stiffness of the entire limb and can be defined by the equations below:
K limb = F max Δ L {\displaystyle K_{\text{limb}}={\frac {F_{\text{max}}}{\Delta L}}}
Where F max is the maximum applied force and ΔL is the change in length of the limb Torsional Stiffness (K_joint) is the rotational stiffness of the joint and can be defined by the equations below:
K joint = Δ M Δ θ {\displaystyle K_{\text{joint}}={\frac {\Delta M}{\Delta \theta }}}
Where ΔM is the change in joint moment and Δθ is the change in joint angle
K joint = 2 W Δ θ {\displaystyle K_{\text{joint}}={\frac {2W}{\Delta \theta }}}
Where W is the negative mechanical work at the joint and Δθ is the change in joint angle These different mathematical definitions of limb stiffness help to describe limb stiffness and show the methods by which such a limb characteristic can be quantified.
Stiffness modulation The human body is able to modulate its limb stiffnesses through various mechanisms with the goal of more effectively interacting with its environment. The body varies the stiffness of its limbs by three primary mechanisms: muscle cocontraction, posture selection, and through stretch reflexes. Muscle cocontraction (similar to muscle tone) is able to vary the stiffness of a joint by the action of antagonistic muscles acting on the joint. The stronger the forces of the antagonistic muscles on the joint are, the stiffer the joint becomes. The selection of body posture also affects the stiffness of the limb. By adjusting the orientation of the limb, the inherent stiffness of the limb can be manipulated. Additionally, the stretch reflexes within a limb can affect the stiffness of the limb, however these commands are not sent from the brain.
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