Dear all,

I wish to clarify the use of stiffness in biomechanics, more specifically “joint stiffness” (and maybe extending to “leg stiffness”). I have read chapters from “Stiffness and Stiffness-like Measures. Latash and Zatsiorsky (2016) Biomechanics and Motor control”, and tried to find some answers in physics textbooks. This seems basic enough, but unfortunately, I do not have a satisfactory answer.

Reason: Traditionally, joint stiffness in gait has been derived using various formulations of the form:

∆momentX/∆CardanAngleX (1)

Where X = one axis, usually flexion-extension axis. However, moment is a vector yet cardan angle is not a vector. Should one be using the vector version of angles (ie angle of rotation X unit vector).

Solutions: If the above is right and meaningful, do we simply perform individual calculations of (1) along each axis to get kX, kY, kZ (assuming 3D only)? Does it make sense to get a kTOTAL using the hypotenuse of the components, to get a single value of 3D stiffness? This is like treating stiffness as a vector.

Alternatively, one can take the hypotenuse of the moment (X,Y,Z) to get a single moment about a joint, take the hypotenuse of joint rotation (vector) and use equation (1), to get a single value of 3D stiffness? .

Any help in clarification or pointing me to relevant articles would be of great help.

Regards,

Bernard

I wish to clarify the use of stiffness in biomechanics, more specifically “joint stiffness” (and maybe extending to “leg stiffness”). I have read chapters from “Stiffness and Stiffness-like Measures. Latash and Zatsiorsky (2016) Biomechanics and Motor control”, and tried to find some answers in physics textbooks. This seems basic enough, but unfortunately, I do not have a satisfactory answer.

__Is “stiffness” based on hook’s law a scalar or vector (https://en.wikipedia.org/wiki/Hooke%27s_law)?__**Qn1:**Reason: Traditionally, joint stiffness in gait has been derived using various formulations of the form:

∆momentX/∆CardanAngleX (1)

Where X = one axis, usually flexion-extension axis. However, moment is a vector yet cardan angle is not a vector. Should one be using the vector version of angles (ie angle of rotation X unit vector).

__What if a coiled spring is deformed in three dimensions (or for that matter 6 directions), how does one calculate deformation force, deformation, and hence “stiffness”? By extension, how do we calculate a joint’s stiffness in 3D (or 6D)? Is it a right thing to do base on physical law? Is it meaningful? In my mind 3D/6D stiffness about a joint would be essential especially in prosthesis development?__**Qn2:**Solutions: If the above is right and meaningful, do we simply perform individual calculations of (1) along each axis to get kX, kY, kZ (assuming 3D only)? Does it make sense to get a kTOTAL using the hypotenuse of the components, to get a single value of 3D stiffness? This is like treating stiffness as a vector.

Alternatively, one can take the hypotenuse of the moment (X,Y,Z) to get a single moment about a joint, take the hypotenuse of joint rotation (vector) and use equation (1), to get a single value of 3D stiffness? .

Any help in clarification or pointing me to relevant articles would be of great help.

Regards,

Bernard

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