In this paper, the invariants of Smarandache curves, which consist Frenet vectors involute curve, are calculated in terms evolute curve.

A procedure to build up a dynamical model of the gearbox with spur involute mesh is being described. The main attention is paid to the design technology of the cylindrical bodies elastic contact models. To track geometry of contact implicit equations of algebraic/transcendental or differential-algebraic type are being used. At the same time dynamical models of the bodies involved, gearwheels an...

The tooth flanks of bevel gears with involute teeth are still cut using approximations such as Tredgold’s and octoid curves, while the geometry of the exact spherical involute is well known. The modeling of the tooth flanks of gears with skew axes, however, still represents a challenge to geometers. Hence, there is a need to develop algorithms for the geometric modeling of these gears. As a mat...

Treatment with antithyroid drugs may be accompanied by side effects. We present a patient diagnosed with Grave's Disease who developed extensive vasculitis in the lower limbs during methimazole use. After suspension of the methimazole and the introduction of prednisone in immunesupressor doses the cutaneous lesions started to involute.

In this work, first, we express some characterizations of helices and ccr curves in the Euclidean 4-space. Thereafter, relations among Frenet-Serret invariants of Bertrand curve of a helix are presented. Moreover, in the same space, some new characterizations of involute of a helix are presented.

In this study, we investigate the semi-real quaternionic curves in the semi-Euclidean space E_4_2. Firstly, we introduce algebraic properties of semi-real quaternions. Then, we give some characterizations of semi-real quaternionic involute-evolute curves in the semi-Euclidean space E42 . Finally, we give an example illustrated with Mathematica Programme.