====== Calculations ======

===== Graphics =====

The following graphics are from the [[https://www.has-motion.com/download/CalTester/CalTesterArticle2003.pdf|CalTester Paper]] Holden JP, Selbie WS, Stanhope SJ, "A proposed test to support the clinical movement analysis laboratory".

{{:Fig1CalTesterArticle.png}}

{{:Fig2CalTesterArticle.png}}

===== Calculations =====

The following calculations and explanations are from the [[https://www.has-motion.com/download/CalTesterPlus/CalTesterArticle2003.pdf|CalTester Paper]] Holden JP, Selbie WS, Stanhope SJ, "A proposed test to support the clinical movement analysis laboratory".\\
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**Section I : Calculating the rod orientation variable under the assumed condition of static equilibrium**\\
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Free-body diagram of testing device: Fp, ground reaction force; Fg, gravitational force (weight); Fa, applied force; r, position vector between tips (p to a) of testing device rod:\\
{{:Calc1CalTesterPlusArticle.png}}\\
Thus, r and A are parallel and the test device rod orientation (r) is defined entirely by the vector quantity A that is derived from FP measurements (Fp) and the physical characteristics of the testing device (Fg/2, i.e.the weight of the rod and its center of mass location; in this case, half the rod length).\\
{{:CalTesterPlus_DeltaTheta.jpg}}\\


The rod orientation variable ( {{:DeltaTheta.jpg}}) is determined from the dot product of the unit vector along A and the unit vector aligned with the long axis of the rod (r) as determined using the motion capture components.\\
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**Section II : Equation for evaluating the static equilibrium assumption**\\


Under 2D dynamic conditions, the following holds:\\
{{:CalTesterPlus_Eq4_v2.jpg}} \\
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Rewriting the left-hand side of Eq. (4)\\
{{:20140107212337caltesterplus_eq5_v2.jpg}} \\
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Rearranging Eq. (5), the magnitude of the angular displacement ( {{:Beta.jpg}} ) between vectors r and A due exclusively to the inertial terms can be isolated:\\
\\
{{:CalTesterPlus_Eq6_v2.jpg}} \\
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where r is the length of the testing device rod, Icg the moment of inertia of the test device rod about the center of mass location, m the mass of the testing device rod and {{:ThetaDoubleDot.jpg}} is the angular acceleration of the testing device rod relative to an inertial reference frame.

CalTesterPlus does not calculate {{:Beta.jpg}} since it operates under the assumption that there is no angular acceleration. For this reason it is important to move the CalTester rod slowly at a constant speed.