An inertial reaction drive in the form of an eccentric rotor is frequently employed in ordnance timing mechanisms. A generalized configuration is analyzed, and the equation of motion is developed. Two examples are given in which the equation of motion is applied to describe the torque output of typical drive configurations.
The method of the “ellipse diagram” previously introduced by the author, for analysis of the motions of spatial mechanisms, is extended. It is then applied to three types of mechanisms, an RSRRR mechanism, a four-bar multi-loop mechanism, and an RPSC mechanism. It is shown that these geometric constructions are also valuable in synthesis because they can predict changes in the motion caused by altering the parameters of a mechanism.
Closed form expressions for the RCRCR mechanism are obtained from dual equations which were derived using spherical trigonometry [1].
An alternative form of the degree four input-output displacement equation obtained by Yang [2] is derived. However, it is demonstrated that the RCRCR mechanism has generally a maximum of eight closures. This result is consistent with the analysis presented in Parts 2 and 3 where eight closures are obtained for both the RRCRC and RCRRC mechanisms.
The analysis for the RCRCR, RRCRC and RCRRC mechanisms is illustrated by plottings of numerical values of linkage variables which were obtained using data common to each inversion.
Analytical expressions have been derived for optimum synthesis of the planar four-bar coupler curve. The method leads to a set of ten simultaneous linear non-homogeneous equations. Solution of these equations yields optimum values for all independent variables in the problem. Application of the present ideas to linkages with six and more links is also outlined. Numerical experience is discussed; it is shown that, for all practical purposes, the optimum is reached after one iterative cycle.
The equations for the velocity and acceleration fields of a rigid body are obtained solely from the definition of an n dimensional projection field.
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