  Decoupled parallel $xyz$ positioning stages with large stroke have been
desired in high-speed and precise positioning fields. However, currently such
stages are either short in stroke or unqualified in parasitic motion and
coupling rate. This paper proposes a novel flexure-based decoupled parallel
$xyz$ positioning stage (FlexDelta) and conducts its conceptual design,
modeling, and experimental study. Firstly, the working principle of FlexDelta
is introduced, followed by its mechanism design with flexure. Secondly, the
stiffness model of flexure is established via matrix-based Castigliano's second
theorem, and the influence of its lateral stiffness on the stiffness model of
FlexDelta is comprehensively investigated and then optimally designed. Finally,
experimental study was carried out based on the prototype fabricated. The
results reveal that the positioning stage features centimeter-stroke in three
axes, with coupling rate less than 0.53%, parasitic motion less than 1.72 mrad
over full range. And its natural frequencies are 20.8 Hz, 20.8 Hz, and 22.4 Hz
for $x$, $y$, and $z$ axis respectively. Multi-axis path tracking tests were
also carried out, which validates its dynamic performance with micrometer
error.
