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.

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.

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.

Finitely and Multiply Separated Synthesis of Link and Geared Mechanisms Using Symbolic Computing

1993 ◽  
Vol 115 (3) ◽  
pp. 560-567 ◽  
Author(s):  
A. K. Dhingra ◽  
N. K. Mani
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Iterative Solution ◽  
Form Solution ◽  
Motion Generation ◽  
Closed Form Solutions ◽  
Symbolic Computing ◽  
Manipulation Language ◽  
Solution Techniques

A computer amenable symbolic computing approach for the synthesis of six different link and geared mechanisms is presented. Burmester theory, complex number algebra, and loop closure equations are employed to develop governing equations for the mechanism to be synthesized. Closed-form and iterative solution techniques have been developed which permit synthesis of six-link Watt and Stephenson chains for function, path, and motion generation tasks with up to eleven precision points. Closed-form solution techniques have also been developed for the synthesis of geared five-bar, six-bar, and five-link cycloidal crack mechanisms, for synthesis tasks with up to six finitely and multiply separated precision points. The symbolic manipulation language MACSYMA is used to simplify the resulting synthesis equations and obtain closed-form solutions. A design methodology which demonstrates the feasibility and versatility of symbolic computing in computer-aided mechanisms design is outlined. A computer program which incorporates these synthesis procedures is developed. Two examples are presented to illustrate the role of symbolic computing in an automated mechanism design process.

A Complex Number Approach for Absolute Precision Position Synthesis for Three Precision Positions

1992 ◽  
Author(s):  
John A. Mirth
Keyword(s):  
Closed Form ◽  
Complex Number ◽  
Closed Form Solution ◽  
Form Solution ◽  
Path Generation ◽  
Motion Generation ◽  
The Absolute ◽  
Position Problem ◽  
Position Synthesis

Abstract Dyads can be synthesized by prescribing the precision point coordinates and the absolute planar orientations of one dyad vector at each of three precision positions. This differs from traditional complex number methods wherein the vector orientations are described relative to one another. Absolute precision position synthesis can be performed for both motion generation, and path generation with prescribed timing. The method presented uses vector loop equations and complex number notation to produce a closed form solution for the three absolute precision position problem. Absolute precision position synthesis is applicable to cases that require specific coupler geometries. The synthesis of flat-folding mechanisms is an example of one such application.

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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