Clark R. Barker

A complete classification of planar four-bar linkages

Abstract A system of classification of planar four-bar mechanisms is presented in which the three major categories are Grashof, non-Grashof and change point. The Grashof and non-Grashof categories are each organized to include four classes while the change point has six classes. The classification system is closely related to a partitioning of the positive octant of a three-dimensional space in which the coordinate axes are nondimensional ratios of the bar lengths. The positive octant is first reduced in size by four zero mobility planes which eliminate from consideration regions where the bar lengths would not permit assembly. The remaining volume is designated as the solution space, and it is partitioned by three change point planes into eight volumes each of which represent a class of Grashof and non-Grashof mechanism. All of the change point classes reside in the change point planes. This paper describes the classification system and the geometry of the solution space, and lays the foundation for future work to study the properties of planar four-bar mechanisms. Because all of the mechanisms within a particular volume share in common characteristics of the bar lengths which are unique to their class, they also share particular properties with regard to the maximum and minimum values of position angles, the range and average value of the position angles, the maximum and minimum value of angular velocity and angular acceleration, as well as time ratio. Hence all of the significant properties can be represented as characteristic surfaces within the solution space. The trace of the characteristic surfaces in the base plane can be used to construct design charts which will permit choosing mechanisms with desirable properties. The method can also be used to synthesize mechanisms by locating intersections of characteristic surfaces. These topics will be presented in forthcoming publications.

Adaptation of Jet Accumulation Techniques for Enhanced Rock Cutting

The velocity of water jet flow can be increased when the jet impacts a target material or another water jet. A theory describing such augmentation in terms of velocity, mass, and energy change is considered. The phenomena is sensitive to jet structure and the jet velocity profile. Jet velocity profiles do not remain constant over great distances from the nozzle, and ultimately disrupt into droplets. Within the droplet the profile is more regular and the velocity constant. The theory is extended to cover this case and experimental evidence of jet augmentation and its effects is presented.

Characteristic surfaces for extreme values of angular velocity ratio in planar four-bar mechanisms

Abstract The extreme values of the angular velocity ratio of a planar four-bar mechanism are considered. A sixth order polynomial is used to find the exact roots for the double change point mechanisms. The range of the extreme values is defined for all of the Grashof cases. Characteristic surfaces are developed which prove to be useful for synthesizing linkages with prescribed extreme values of angular velocity ratio.