First-Order Coordination of the Articulated Arm Subassembly Using Curvature Theory

2007 ◽  
Author(s):  
Satyajit Ambike ◽  
James P. Schmiedeler
Keyword(s):  
Taylor Series ◽  
Direct Method ◽  
Joint Coordination ◽  
First Order ◽  
Spatial Mechanisms ◽  
Canonical Frame ◽  
Curvature Theory ◽  
Three Degree Of Freedom ◽  
A Direct Method ◽  
Invariants Of Motion

This paper presents an approach to obtain the first-order speed ratios for three-degree-of-freedom spatial mechanisms that allow three degrees of translational freedom. The approach eliminates the need to locate the canonical frame and find the instantaneous invariants of motion and provides a direct method of obtaining the first-order speed ratios. The expressions for the speed ratios of the articulated arm subassembly are analyzed, and the regions of the workspace wherein the joints have dwells in their trajectories are identified. The first-order Taylor series is used for joint coordination, allowing the system to track a predefined spatial path. An example illustrating the application of curvature theory to spatial path tracking with a specific articulated arm subassembly is presented.

Direct Method for Determining Inorganic Phosphate in Serum with the "CentrifiChem"

1972 ◽  
Vol 18 (3) ◽  
pp. 263-265 ◽  
Author(s):  
John A Daly ◽  
Gerhard Ertingshausen
Keyword(s):  
Inorganic Phosphate ◽  
Direct Method ◽  
Order Reaction ◽  
First Order Reaction ◽  
First Order ◽  
Kinetics Of ◽  
A Direct Method

Abstract A direct method was developed for determining inorganic phosphate in serum, which requires only a single reagent addition. The method quantitates the unreduced phosphomolybdate heteropolyacid at 340 nm and is linear to at least 10 mg of phosphate per 100 ml. Only 10 µl of serum is required. The unique blanking capabilities of centrifugal analyzers permit the "on run" elimination of serum and reagent background absorbances, which are automatically subtracted. Data on precision, correlation, and recovery are presented. Kinetics of the reaction were studied, and theoretical limits of automatic blanking when applied to a first-order reaction are discussed.

A relative consistency proof

1954 ◽  
Vol 19 (1) ◽  
pp. 21-28 ◽  
Author(s):  
Joseph R. Shoenfield
Keyword(s):  
Set Theory ◽  
Functional Calculus ◽  
Direct Method ◽  
Axiom System ◽  
Similar Process ◽  
Consistency Proof ◽  
First Order ◽  
Definition Of ◽  
A Direct Method ◽  
Exact Definition

LetCbe an axiom system formalized within the first order functional calculus, and letC′ be related toCas the Bernays-Gödel set theory is related to the Zermelo-Fraenkel set theory. (An exact definition ofC′ will be given later.) Ilse Novak [5] and Mostowski [8] have shown that, ifCis consistent, thenC′ is consistent. (The converse is obvious.) Mostowski has also proved the stronger result that any theorem ofC′ which can be formalized inCis a theorem ofC.The proofs of Novak and Mostowski do not provide a direct method for obtaining a contradiction inCfrom a contradiction inC′. We could, of course, obtain such a contradiction by proving the theorems ofCone by one; the above result assures us that we must eventually obtain a contradiction. A similar process is necessary to obtain the proof of a theorem inCfrom its proof inC′. The purpose of this paper is to give a new proof of these theorems which provides a direct method of obtaining the desired contradiction or proof.The advantage of the proof may be stated more specifically by arithmetizing the syntax ofCandC′.

scholarly journals Plastic waste to fuels by hydrocracking at mild conditions

2021 ◽  
Vol 7 (17) ◽  
pp. eabf8283
Author(s):  
Sibao Liu ◽  
Pavel A. Kots ◽  
Brandon C. Vance ◽  
Andrew Danielson ◽  
Dionisios G. Vlachos
Keyword(s):  
Direct Method ◽  
Acid Sites ◽  
Liquid Fuels ◽  
High Yield ◽  
Tandem Catalysis ◽  
Hy Zeolite ◽  
Environmental Threat ◽  
Single Use ◽  
Initial Activation ◽  
A Direct Method

Single-use plastics impose an enormous environmental threat, but their recycling, especially of polyolefins, has been proven challenging. We report a direct method to selectively convert polyolefins to branched, liquid fuels including diesel, jet, and gasoline-range hydrocarbons, with high yield up to 85% over Pt/WO3/ZrO2 and HY zeolite in hydrogen at temperatures as low as 225°C. The process proceeds via tandem catalysis with initial activation of the polymer primarily over Pt, with subsequent cracking over the acid sites of WO3/ZrO2 and HY zeolite, isomerization over WO3/ZrO2 sites, and hydrogenation of olefin intermediates over Pt. The process can be tuned to convert different common plastic wastes, including low- and high-density polyethylene, polypropylene, polystyrene, everyday polyethylene bottles and bags, and composite plastics to desirable fuels and light lubricants.

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