Analytical Reason for Smaller Lateral Sway in Angled-Plane Scissor Linkage

2020 ◽  
Vol 12 (5) ◽  
Author(s):  
Sunil Kumar Singh ◽  
Sangamesh R. Deepak
Keyword(s):  
Rigid Body ◽  
Optimization Problem ◽  
Linear Optimization ◽  
Parallel Plane ◽  
Design Parameters ◽  
Finite Limit ◽  
Constrained Optimization Problem ◽  
Linear Optimization Problem ◽  
Non Linear ◽  
Linear Constrained Optimization

Abstract Scissor linkages are widely used with scissor links arranged in two parallel planes. When small misalignment of revolute joint axes are permissible, the linkage can undergo lateral sway. This paper, using rigid-body kinematics and a modeling of misalignment, converts the task of finding lateral sway into a non-linear constrained optimization problem. Through linearization of the optimization problem, this paper analytically proves that (1) maximum lateral sway increases as the number of units in the parallel-plane scissor linkage increases whereas in angled-plane scissor linkage, the lateral sway tends to a finite limit as the number of units is increased and (2) the lateral sway is independent of connector length in parallel-plane scissor linkage whereas it is dependent on the length of the connector in angled-plane scissor linkage. These results are further substantiated with numerical solution of the non-linear optimization problem. The results imply that the angled-plane scissor linkage can substantially limit lateral sway in comparison to parallel-plane scissor linkage under similar conditions of joint misalignment. The analytical expression derived in this paper helps in identifying the influence of design parameters on lateral sway.

scholarly journals Algebraic Bayesian network: non-linear optimization problem in local posteriori inference with atomic stochastic evidence

2014 ◽  
Vol 1 (20) ◽  
pp. 200
Author(s):  
Alexander Vladimirovich Sirotkin ◽  
Valeriya Fuatovna Musina ◽  
Alexander Lvovich Tulupyev
Keyword(s):  
Bayesian Network ◽  
Optimization Problem ◽  
Linear Optimization ◽  
Linear Optimization Problem ◽  
Non Linear

Four-bar motion generation with elasticity constraints and optimization

2009 ◽  
Vol 223 (3) ◽  
pp. 245-253
Author(s):  
Y M Al-Smadi ◽  
K Russell ◽  
R S Sodhi
Keyword(s):  
Optimization Problem ◽  
Search Algorithm ◽  
Linear Optimization ◽  
Motion Generation ◽  
Linear Optimization Problem ◽  
Transmission Angle ◽  
Non Linear ◽  
Transverse Deflection ◽  
Static Torque ◽  
Motion Generator

In conventional planar four-bar motion generation, all mechanism links are assumed rigid or non-deforming. Although the assumption of link rigidity in kinematic synthesis may be generally appropriate and often practiced, a statically loaded planar four-bar mechanism will undergo a degree of elastic deflection, particularly the crank and follower links. In this work, a non-linear optimization problem is formulated for planar four-bar motion generation that considers an applied coupler force and corresponding crank static torque, crank transverse deflection, and follower buckling. The output from the non-linear optimization problem – mechanism fixed and moving pivot loci – are input for a search algorithm that down selects a mechanism solution that satisfies transmission angle conditions, Grashof conditions, and a mechanism compactness condition. The final output of the presented method is planar four-bar motion generator that approximates prescribed coupler poses with satisfactory crank deflection and without follower buckling and also satisfies conditions for link rotatability, transmission angle and compactness.

Teeth-Number Synthesis of an Automatic Planetary Transmission Using Evolutionary Computation

2004 ◽  
Author(s):  
P. A. Simionescu ◽  
D. G. Beale ◽  
G. V. Dozier
Keyword(s):  
Constrained Optimization ◽  
Objective Function ◽  
Evolutionary Computation ◽  
Optimization Problem ◽  
Design Parameters ◽  
Constrained Optimization Problem ◽  
Gear Teeth ◽  
Estimation Of Distribution ◽  
Number Synthesis ◽  
Planetary Transmission

The gear-teeth number synthesis of an automatic planetary transmission used in automobiles is formulated as a constrained optimization problem that is solved with the aid of an Estimation of Distribution Algorithm. The design parameters are the teeth number of each gear, the number of multiple planets and gear module, while the objective function is defined based on the departure between the imposed and the actual gear ratios, constrained by teeth-undercut avoidance, limiting the maximum overall diameter of the transmission and ensuring proper planet spacing.

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