Academic literature on the topic 'Geometric sewing'

The mathematical functions associated with analytic elements may be formulated using a complex function $\Omega$ of a complex variable ${\zcomplex}$. Complex formulation of analytic elements is introduced in Section 3.1 for exact solutions obtained by embedding point elements that generate divergence, circulation, or velocity within a uniform vector field. Influence functions for analytic elements with circular geometry are obtained using Taylor and Laurent series expansions in Section 3.2, and conformal mapping extends this formulation to analytic elements with the geometry of ellipses (Section 3.3). The Courant's Sewing Theorem is employed in Section 3.4 to develop solutions for interface conditions across straight line segments, and the Joukowsky transformation extends methods to circular arcs and wings (Section 3.5), which satisfy a Kutta condition of non-singular vector field at their trailing edges. Vector fields with spatially distributed divergence and curl are formulated using the complex variable ${\zcomplex}$ with its complex conjugate $\overline{\zcomplex}$ in Section 3.6, and the complex conjugate is further employed in the Kolosov formulas (Section 3.7) to solve force deformation problems for analytic elements with traction or displacement specified boundary conditions.

A recently emerged artificial muscle that is created by transforming a sewing thread or fishing line through a process of twisting, coiling and annealing has a great potential application in sensing, actuation or energy harvesting. Extensive experimental investigations along with modeling have been carried out to further understand the twisted and coiled polymer (TCP) muscle. The TCP muscle has a large actuation stroke and long life cycle, and is easy to produce with low cost. Incorporation of TCP muscles into sensor application will advance the combined muscle-sensor integrated system develop