## Abstract

It is a well-known result of instantaneous spherical kinematics that the locus of those points of the moving sphere, whose paths have a vanishing geodesic curvature, is a curve w on a cubic cone Ω with vertex in the center O of the sphere. In this paper we give a simple construction of the inflection curve w using the following theorem: The intersecting curve l of the inflection cone Ω with a sphere κ, which is centered on the pole-axis p and contains the point O, lies on a cylinder of revolution. This cylinder contains the inflection circle of that planar motion in the tangent plane τ of κ in the pole P = p ∩ κ (P ≠ O), whose relationship between the points and centers of curvature of their paths is induced in τ by the spherical motion. Furthermore we use this result to draw some geometrical conclusions on the set of the ∞^{1} inflection curves belonging to a given canonical frame. In a special case the inflection curve is a spherical trochoid.

Original language | German |
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Pages (from-to) | 77-79 |

Number of pages | 3 |

Journal | Mechanism and Machine Theory |

Volume | 20 |

Issue number | 1 |

DOIs | |

State | Published - 1985 |

Externally published | Yes |

## ASJC Scopus subject areas

- Bioengineering
- Mechanics of Materials
- Mechanical Engineering
- Computer Science Applications