Finite Kinematic Synthesis of a Cycloidal-Crank Mechanism for Function Generation

1970 ◽  
Vol 92 (3) ◽  
pp. 531-535 ◽  
Author(s):  
S. N. Kramer ◽  
G. N. Sandor
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Optimization Method ◽  
Gear Ratio ◽  
Form Solution ◽  
Complex Numbers ◽  
Kinematic Synthesis ◽  
Function Generation ◽  
Approximate Function ◽  
Crank Mechanism

The method of complex numbers is applied towards the kinematic synthesis of a planar geared five-bar cycloidal-crank mechanism for approximate function generation with finitely separated precision points. It is shown that up to 10 precision points can be obtained, and a closed-form solution is presented which yields up to 6 different mechanisms with a 6-point approximation. In this method, the designer has control over the design of the cycloidal crank regarding gear ratio and configuration. The method has been programmed for automatic digital computation on the IBM-360 system, and the program is made available to interested readers. An optimization method utilizing iterative application of the closed-form solution is outlined.

scholarly journals A Closed-Form Solution for Estimating the Accuracy of Circular Feature’ Pose for Object 2D-3D Pose Estimation System

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Cui Li ◽  
Derong Chen ◽  
Jiulu Gong ◽  
Yangyu Wu
Keyword(s):  
Closed Form ◽  
Covariance Matrix ◽  
Pose Estimation ◽  
Closed Form Solution ◽  
Optimization Method ◽  
Form Solution ◽  
Synthetic Image ◽  
Point Selection ◽  
3D Pose Estimation ◽  
Estimation System

Many objects in the real world have circular feature. In general, circular feature’s pose is represented by 5-DoF (degree of freedom) vector ξ = X , Y , Z , α , β T . It is a difficult task to measure the accuracy of circular feature’s pose in each direction and the correlation between each direction. This paper proposes a closed-form solution for estimating the accuracy of pose transformation of circular feature. The covariance matrix of ξ is used to measure the accuracy of the pose. The relationship between the pose of the circular feature of 3D object and the 2D points is analyzed to yield an implicit function, and then Gauss–Newton theorem is employed to compute the partial derivatives of the function with respect to such point, and after that the covariance matrix is computed from both the 2D points and the extraction error. In addition, the method utilizes the covariance matrix of 5-DoF circular feature’s pose variables to optimize the pose estimator. Based on pose covariance, minimize the mean square error (Min-MSE) metric is introduced to guide good 2D imaging point selection, and the total amount of noise introduced into the pose estimator can be reduced. This work provides an accuracy method for object 2D-3D pose estimation using circular feature. At last, the effectiveness of the method for estimating the accuracy is validated based on both random data sets and synthetic images. Various synthetic image sequences are illustrated to show the performance and advantages of the proposed pose optimization method for estimating circular feature’s pose.

Analysis and Optimal Synthesis of the RSCR Spatial Mechanism

1991 ◽  
Author(s):  
G. K. Ananthasuresh ◽  
Steven N. Kramer
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Optimization Method ◽  
Form Solution ◽  
Mechanism Analysis ◽  
Motion Generation ◽  
Spatial Mechanism ◽  
Geometric Characteristics ◽  
Nonlinear Inequality ◽  
Nonlinear Inequality Constraints

Abstract The closed form solution of the analysis of the RSCR (Revolute-Spherical-Cylindrical-Revolute) spatial mechanism is presented in this paper. This work is based on the geometric characteristics of the mechanism involving the following three cases: the cone, the cylinder and the one-sheet hyperboloid. These cases derive their names from the nature of the locus of the slider of the linkage as viewed from the output side. Each case is then treated separately to develop a closed form, geometry based analysis technique. These analysis modules are then used to optimally synthesize the mechanism for function, path and motion generation problems satisfying precision conditions within prescribed accuracy limits. The Selective Precision Synthesis technique is employed to formulate the nonlinear inequality constraints. These constraints along with an objective function and other constraints are solved using the Generalized Reduced Gradient method of optimization. In addition, the use of mobility charts is used to aid the designer in making a judicious choice for the initial design point before invoking the optimization method. The determination of the transmission angle for the RSCR mechanism is also described and numerical examples for function, path and motion generation are also included. This new closed form method of analysis based on geometric characteristics is computationally less intensive than other available techniques for spatial mechanism analysis and helps in the visualization of the physical mechanism; something that is not possible with most vector and matrix methods.

Analysis and Optimal Synthesis of the RSCR Spatial Mechanisms

1994 ◽  
Vol 116 (1) ◽  
pp. 174-181 ◽  
Author(s):  
G. K. Ananthasuresh ◽  
S. N. Kramer
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Optimization Method ◽  
Form Solution ◽  
Mechanism Analysis ◽  
Motion Generation ◽  
Spatial Mechanism ◽  
Geometric Characteristics ◽  
Nonlinear Inequality ◽  
Nonlinear Inequality Constraints

A closed form solution of the analysis of the RSCR (Revolute-Spherical-Cylindrical-Revolute) spatial mechanism is presented in this paper. This work is based on the geometric characteristics of the mechanism involving the following three cases: the cone, the cylinder, and the one-sheet hyperboloid. These cases derive their names from the nature of the locus of the slider of the linkage as viewed from the output side. Each case is then treated separately to develop a closed form, geometry based analysis technique. These analysis modules are then used to optimally synthesize the mechanism for function, path and motion generation problems satisfying precision conditions within prescribed accuracy limits. The Selective Precision Synthesis technique is employed to formulate the nonlinear inequality constraints. These constraints along with an objective function and other constraints are solved using the Generalized Reduced Gradient method of optimization. In addition, mobility charts are used to aid the designer in making a judicious choice for the initial design point before invoking the optimization method. Numerical examples are presented to validate the theory. This new closed form method of analysis that is based on geometric characteristics is computationally less intensive than other available techniques for spatial mechanism analysis and helps in the visualization of the physical mechanism; something that is not possible with most vector and matrix methods.

A Closed-Form Solution to the Crank Position Corresponding to the Maximum Velocity of the Slider in a Centric Slider-Crank Mechanism

2005 ◽  
Vol 128 (3) ◽  
pp. 654-656 ◽  
Author(s):  
W. J. Zhang ◽  
Q. Li
Keyword(s):  
Closed Form ◽  
Classical Problem ◽  
Closed Form Solution ◽  
Maximum Velocity ◽  
Form Solution ◽  
Machine Design ◽  
Rotary Engine ◽  
Engine Systems ◽  
Crank Mechanism

This paper revisits a classical problem in kinematics, specifically determination of the crank position corresponding to the maximum velocity of the slider in the centric slider-crank mechanism. This position is often critical in designing products constructed using the slider-crank mechanism, e.g., industrial sewing machinery, rotary engine systems, etc. In current literature, the numerical, graphical, or approximate closed-form solution to this problem is available. In this paper, an exact closed-form solution is derived. With this new closed-form solution, it is found that there exist significant errors in an approximate closed-form solution which can be found from many machine design text books for a practica1 use.

Kinematic Synthesis of a Geared Five-Bar Function Generator

1971 ◽  
Vol 93 (1) ◽  
pp. 11-16 ◽  
Author(s):  
Arthur G. Erdman ◽  
George N. Sandor
Keyword(s):  
Computer Program ◽  
Closed Form ◽  
Complex Numbers ◽  
Function Generator ◽  
Kinematic Synthesis ◽  
Numerical Examples ◽  
Function Generation ◽  
Structural Error ◽  
Dependent Variables ◽  
Angular Displacements

A general closed form method of planar kinematic synthesis, using complex numbers to represent link vectors, is applied to the synthesis of a geared five-bar linkage for function generation. Equations are derived and a computer program is developed to yield several solutions. Angular displacements of the input, a cycloidal crank, and the output, a simple follower, are used as linear analogs of the independent and the dependent variables, respectively. A method is demonstrated for six precision conditions (three first, three second-order precision conditions). Numerical examples are included, and the structural error of these geared five-bars are compared to that of optimized four-bar linkages generating the same functions.

On a Closed-Form Solution of Prandtl's System of Equations

2013 ◽  
Vol 40 (2) ◽  
pp. 106-114
Author(s):  
J. Venetis ◽  
Aimilios (Preferred name Emilios) Sideridis
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
System Of Equations
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