Abstract In this paper, some new integral curves are defined in three-dimensional Euclidean space by using a new frame of a polynomial spatial curve. The Frenet vectors, curvature and torsion of these curves are obtained by means of new frame and curvatures. We give the characterizations and properties of these integral curves under which conditions they are general helix. Also, the relationships between these curves in terms of being some kinds of associated curves are introduced. Finally, an example is illustrated.

中文翻译：

---

一些带有新框架的积分曲线

摘要 本文利用多项式空间曲线的新坐标系，在三维欧几里得空间中定义了一些新的积分曲线。这些曲线的 Frenet 矢量、曲率和扭转是通过新的框架和曲率获得的。我们给出了这些积分曲线在什么条件下它们是一般螺旋的特征和性质。此外，还介绍了这些曲线之间作为某种关联曲线的关系。最后，举例说明。