Identification of Non-Transversal Motion Bifurcations of Linkages

The local analysis is an established approach to the study of singularities and mobility of linkages. The key result of such analyses is a local picture of the finite motion through a configuration. This reveals the finite mobility at that point and the tangents to smooth motion curves. It does, however, not immediately allow to distinguish between motion branches that do not intersect transversally (which is a rather uncommon situation that has only recently been discussed in the literature). The mathematical framework for such a local analysis is the kinematic tangent cone. It is shown in this paper that the constructive definition of the kinematic tangent cone already involves all information necessary to distinguish different motion branches. A computational method is derived by amending the algorithmic framework reported in previous publications.

Identification of Non-Transversal Bifurcations of Linkages

The local analysis is an established approach to the study of singularities and mobility of linkages. Key result of such analyses is a local picture of the finite motion through a configuration. This reveals the finite mobility at that point and the tangents to smooth motion curves. It does, however, not immediately allow to distinguish between motion branches that do not intersect transversally (which is a rather uncommon situation that has only recently been discussed in the literature). The mathematical framework for such a local analysis is the kinematic tangent cone. It is shown in this paper that the constructive definition of the kinematic tangent cone already involves all information necessary to separate different motion branches. A computational method is derived by amending the algorithmic framework reported in previous publications.

Projectile Motion in a Vacuum According to Francesc Marbres, Francis of Marchia, Gerald Odonis, and Nicholas Bonet

In the third decade of the fourteenth century, the first definitive steps were taken to replace Aristotle’s theory of projectile motion and to apply the new theory to explain finite motion in a vacuum. The main actors in this shift were the Franciscan theologians Francis of Marchia, Gerald Odonis, and Nicholas Bonet, as well as Francesc Marbres, the artist formerly known as ‘John the Canon,’ but there is some confusion about their respective roles. Over the past decade, critical editions and manuscript studies of the pertinent texts of Marchia, Odonis, and Marbres have provided the raw materials to straighten out what some have considered the early background to the Galilean theory of projectile motion.

Investigation of a Cylindroid Engendered by the Bennett Linkage

Most studies of the Bennett linkage over the past century have been concerned with the characteristics of its instantaneous motion, revealing a large number of features and relationships. Latterly, work has been carried out on properties of the finite motion, an evidently separate area of consideration. However, there is one item of commonality between the two zones of activity, namely, the instantaneous screw axis of the loop's coupler. This fact is directed towards the employment of results from the former area of study to the benefit of the latter.