Table 17.

Variable definitions, values, and source for validating spring selection.

Variable	Definition	Value	Source
$d_m$	Mean screw diameter	7 $\times$ 10-3 m	Leadscrew property
$\theta$	Thread angle	15°	Leadscrew property
$l$	Leadscrew lead	8 $\times$ 10-3 m	Leadscrew property
$f_s$	Starting friction of brass nut	0.30	Tabulated value [23]
$T_{escape}$	Escapement starting torque	5.4 $\times$ 10-4 N m	Measured (see Section 7.3)
$F_d$	Force to deliver 1.0 $\times$ 10-6 l in 1  s	0.8 N	Estimated (see Appendix)
$FOS$	Factor of safety	1.5	Design parameter
$x_{min}$	Minimum spring compression	12.0 $\times$ 10-3 m	Design parameter
$x_{max}$	Maximum spring compression	40.0 $\times$ 10-3 m	Design parameter
$d$	Spring wire diameter	1 $\times$ 10-3 m	Spring property
$G$	Shear modulus	79.3 $\times$ 109 N m−2	Tabulated value for steel [24]
$D$	Mean spring diameter	13 $\times$ 10-3 m	Spring property
$N$	Number of active spring coils	9	Spring property
$A_{res}$	Cross-sectional area of reservoir	1.13 $\times$ 10-4 m2	Reservoir property