Kinematic analysis of cardan drives

Abstract

The method for kinematic analysis, known since the 1930s [1], has not been imposed in practice. In recent papers the exact equations, proposed in Ref. [1], have been replaced by approximate ones [2–4]. Graphic methods have been created [5, 6] for the synthesis of cardan drives. The approximate analytical and graphic methods do not reveal the properties and the peculiarities of cardan drives and do not suggest the way for their improvement. No exact mathematical method for kinematic analysis and synthesis of cardan drives has been proposed. In some works (e.g. Ref. [6]) the equivalent (resultant) angle is discussed, but no attempt has been made to derive the basic equation of the equivalent cardan mechanism. No method has been proposed for the synthesis of optimal cardan drives. We cannot agree with the proposition in Ref. [6] that if the equivalent angle is zero the optimal angular positioning of the forks is achieved. This problem is not so simple, as presented in Ref. [6]. In the present work we have derived the basic equation of the equivalent cardan mechanism and used the determination of the equivalent angle. The equation of the gear-function has also been obtained. Consequently, the opinion that the theory of cardan drives has already been developed and nothing could be added to it, is inconsistent. The new theory of cardan drives, proposed in this paper, has been initially outlined in Ref. [7]. The aim of the paper is to acquaint the readers with the fundamentals of the new theory and the new methods for kinematic analysis and synthesis of optimal cardan drives.