A method for completely balancing the shaking forces and shaking moments in mechanisms is presented. The method introduces shaking moment balancing idler parallelogram loop (or loops) which transfers the motion of a coupler link to a shaft on the frame of the mechanism, where the rotary balancers balance the shaking moment. The complete balancing of a mechanism is accomplished by maintaining the total center of mass of the mechanism stationary meanwhile achieving that the total angular momentum of the moving links of the mechanism vanishes. Positioning of the idler loops is illustrated for a series of multiloop mechanisms. Theorems on the complete balancing of shaking forces and shaking moments in mechanisms are established. Design equations for completely balancing some single and multiloop mechanisms are given. A numerical example is included.
The general form of the mobility equation is presented, which predicts the number of inputs required to drive a multiloop mechanism having redundant freedoms, passive freedoms, different general constraints in different loops, and groups of loops having over-closing constraints. Redundant freedoms, passive freedoms, general constraints, over-closing constraints are described, and the use of the mobility equation is illustrated through numerous examples. A method of identifying the class of a mechanism is also given.
The effect of the film shape on the load carrying capacity of a hydrodynamically lubricated bearing has not been considered an important factor in the past. Flat-faced tapered bearing and the Raileigh’s step bearing of constant film thickness have been the primary forms of film shapes for slider bearing studies and design data developments. This article, by the computer aided numerical solution of the Reynolds equation for two dimensional incompressible lubricant flow, investigates hydrodynamically lubricated slider bearings having different film shapes and studies the effect of the film shape on the performance characteristics of finite bearings; and it shows that optimized bearing with film shapes having descending slope toward the trailing edge of the bearing has considerably higher load carrying capacity than the optimized flat-faced tapered bearing of the same properties. For example the truncated cycloidal film shape yields 26.3 percent higher load carrying capacity for Lz/Lx = 1 size ratio, and 44 percent higher for Lz/Lx = 1/2. The article then presents charts for the optimum designs of finite slider bearings having tapered, exponential, catenoidal, polynomial, and truncated-cycloidal film shapes, and illustrates their use in numerical bearing design examples. These charts also furnish information on flow rate, side leakage, temperature rise, coefficient of friction, and friction power loss in optimum bearings. Appended to the article are analytical solutions for infinitely wide bearings with optimum bearing characteristics. The computer aided numerical solution of the Reynolds equation in most general form is presented by which finite or infinitely wide hydrodynamically or hydrostatically lubricated bearings, externally pressurized or not, can be studied. A digital computer program is made available.
Complete balancing of shaking forces and shaking moments in space mechanisms is the subject of this article. Using real vectors, it presents methods of balancing shaking forces completely in space mechanisms. Force balancing of a mechanism is achieved by attaining a stationary center of the total mass of the mechanism. Design equations for force balancing of the RSSR, RSSP slider-crank and RSRC, CSC, and RCRC screw generators are developed. These mechanisms, their pair inversion mechanisms are force balanced thus establishing general guidelines for force balancing of space mechanisms. It is shown that SC and SRC dyads in space mechanisms also introduce force transmission irregularity in addition to the CRC, CCC, CRP, PRP, PSP, PSC dyads that introduce force transmission irregularity. Space mechanisms with force transmission irregularities are balanced by attaching a force balancing RRR dyad or a linearly moving conterbalancer driven by gear-rack drive, a belt, chain, or rolomite mechanism.
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