We introduce the Study variety of conformal kinematics and investigate some of its properties. The Study variety is a projective variety of dimension ten and degree twelve in real projective space of dimension 15, and it generalizes the well-known Study quadric model of rigid body kinematics. Despite its high dimension, co-dimension, and degree it is amenable to concrete calculations via conformal geometric algebra (CGA) associated to three-dimensional Euclidean space. Calculations are facilitated by a four quaternion representation which extends the dual quaternion description of rigid body kinematics. In particular, we study straight lines on the Study variety. It turns out that they are related to a class of one-parametric conformal motions introduced by Dorst in (Math Comput Sci 10:97–113, 2016, https://doi.org/10.1007/s11786-016-0250-8). Similar to rigid body kinematics, straight lines (that is, Dorst’s motions) are important for the decomposition of rational conformal motions into lower degree motions via the factorization of certain polynomials with coefficients in CGA.

我们介绍了保形运动学的研究品种，并研究了它的一些特性。Study 变体是 15 维实射影空间中的 10 维和 12 次射影变体，它推广了著名的刚体运动学 Study 二次模型。尽管它具有高维、共维和度数，但它可以通过与三维欧几里得空间相关的共形几何代数 (CGA) 进行具体计算。四个四元数表示有助于计算，它扩展了刚体运动学的对偶四元数描述。特别是，我们研究了 Study 品种上的直线。事实证明，它们与 Dorst 在 (Math Comput Sci 10:97–113, 2016, https://doi.org/10.1007/s11786-016-0250-8) 中引入的一类单参数保形运动有关.