AN INTUITIVE APPROACH TO THE KINEMATIC SYNTHESIS OF MECHANISMS

2016 ◽  
Author(s):  
Bruno Fausto Zappa ◽  
Vittorio Lorenzi ◽  
Paolo Righettini ◽  
Roberto Strada
Keyword(s):  
Kinematic Synthesis ◽  
Synthesis Of Mechanisms

A frame-independent comparison metric for discrete motion sequences

2020 ◽  
Vol 234 (9) ◽  
pp. 1764-1774
Author(s):  
Ping Zhao ◽  
Yong Wang ◽  
Lihong Zhu ◽  
Xiangyun Li
Keyword(s):  
Moving Frame ◽  
Kinematic Synthesis ◽  
Reference Motion ◽  
Comparison Results ◽  
Synthesis Of Mechanisms ◽  
Rotational Part ◽  
The Difference ◽  
Four Bar Linkage ◽  
The Given ◽  
Discrete Motion

To evaluate the kinematic performance of designed mechanisms, a statistical-variance-based metric is proposed in this article to measure the “distance” between two discrete motion sequences: the reference motion and the given task motion. It seeks to establish a metric that is independent of the choice of the fixed frame or moving frame. Quaternions are adopted to represent the rotational part of a spatial pose, and the variance of the set of relative displacements is computed to reflect the difference between two sequences. With this variance-based metric formulation, we show that the comparison results of two spatial discrete motions are not affected by the choice of frames. Both theoretical demonstration and computational example are presented to support this conclusion. In addition, since the deviation error between the task motion and the synthesized motion measured with this metric is independent of the location of frames, those corresponding parameters could be excluded from the optimization algorithm formulated with our frame-independent metric in kinematic synthesis of mechanisms, and the complexity of the algorithm are hereby reduced. An application of a four-bar linkage synthesis problem is presented to illustrate the advantage of the proposed metric.

scholarly journals Synthesis of Mechanisms by Methods of Nonlinear Dynamics

10.14311/1684 ◽  
2012 ◽  
Vol 52 (6) ◽  
Author(s):  
Michael Valášek ◽  
Zbynek Šika
Keyword(s):  
Dynamical System ◽  
Dissipative System ◽  
New Method ◽  
Time Varying ◽  
Objective Functions ◽  
Mechanism Synthesis ◽  
Kinematic Synthesis ◽  
Nonlinear Dynamical ◽  
Synthesis Of Mechanisms ◽  
Synthesis Procedure

This paper deals with a new method for parametric kinematic synthesis of mechanisms. The traditional synthesis procedure based on collocation, correction and optimization suffers from the local minima of objective functions, usually due to the local unassembled configurations which must be overcome. The new method uses the time varying values of the synthesized dimensions of the mechanism as if the mechanism had elastic links and guidances. The time varying dimensions form the basis for an accompanying nonlinear dynamical dissipative system and the synthesis is transformed into the time evolution of this accompanying dynamical system. Its dissipativity guarantees the termination of thesynthesis. The synthesis always covers the parametric kinematic synthesis, but it can be advantageously extended into the optimization of any further criteria. The main advantage of the method described here for dealing with mechanism synthesis is that it overcomes the unassembled configurations of the synthesized mechanisms and enables any further synthesis criteria to be introduced, and terminates due to dissipation of the accompanied dynamical system.

Application of Instantaneous Invariants to the Analysis and Synthesis of Mechanisms

1977 ◽  
Vol 99 (1) ◽  
pp. 97-103 ◽  
Author(s):  
B. Roth ◽  
A. T. Yang
Keyword(s):  
Problem Solving ◽  
Rigid Body ◽  
Rigid Body Motion ◽  
Geometric Constraint ◽  
Body Motion ◽  
Kinematic Synthesis ◽  
Systematic Procedure ◽  
Synthesis Of Mechanisms ◽  
Analysis And Synthesis ◽  
Kinematic Properties

The objective of this paper is to make instantaneous invariants a more accessible tool for problem solving in the field of kinematics. We present a systematic procedure to determine the instantaneous invariants of a rigid body under geometric constraint, develop a process by which kinematic properties of rigid body motion can be expressed in terms of instantaneous invariants, and apply instantaneous invariants to solve typical kinematic synthesis problems. Four examples are given in detail for illustrative purposes.

New Complex-Number Forms of the Euler-Savary Equation in a Computer-Oriented Treatment of Planar Path-Curvature Theory for Higher-Pair Rolling Contact

1982 ◽  
Vol 104 (1) ◽  
pp. 227-232 ◽  
Author(s):  
G. N. Sandor ◽  
A. G. Erdman ◽  
L. Hunt ◽  
E. Raghavacharyulu
Keyword(s):  
Complex Number ◽  
Rolling Contact ◽  
Radius Of Curvature ◽  
Planar Mechanisms ◽  
Kinematic Synthesis ◽  
Synthesis Of Mechanisms ◽  
Curvature Theory ◽  
Path Curvature ◽  
Planar Linkages ◽  
Contact Mechanism

It is well known from the theory of Kinematic Synthesis of planar mechanisms that the Euler-Savary Equation (ESE) gives the radius of curvature and the center of curvature of the path traced by a point in a planar rolling-contact mechanism. It can also be applied in planar linkages for which equivalent roll-curve mechanisms can be found. Typical example: the curvature of the coupler curve of a four-bar mechanism. Early works in the synthesis of mechanisms concerned themselves with deriving the ESE by means of combined graphical and algebraic techniques, using certain sign conventions. These sign conventions often become sources of error. In this paper new complex-number forms of the Euler-Savary Equation are derived and are presented in a computer-oriented format. The results are useful in the application of path-curvature theory to higher-pair rolling contact mechanisms, such as cams, gears, etc., as well as linkages, once the key parameters of an equivalent rolling-contact mechanism are known. The complex-number technique has the advantage of eliminating the need for the traditional sign conventions and is suitable for digital computation. An example is presented to illustrate this.

Computational Creativity via Assisted Variational Synthesis of Mechanisms Using Deep Generative Models

2019 ◽  
Author(s):  
Shrinath Deshpande ◽  
Anurag Purwar
Keyword(s):  
Probability Distribution ◽  
Computational Methods ◽  
Network Architecture ◽  
Generative Models ◽  
Motion Generation ◽  
Kinematic Synthesis ◽  
User Input ◽  
Synthesis Of Mechanisms ◽  
End To End ◽  
Salient Features

Abstract Computational methods for kinematic synthesis of mechanisms for motion generation problems require input in the form of precision positions. Given the highly non-linear nature of the problem, solutions to these methods are overly sensitive to the input — a small perturbation to even a single position of a given motion can change the topology and dimensions of the synthesized mechanisms drastically. Thus, the synthesis becomes a blind iterative process of maneuvering precision positions in the hope of finding good solutions. In this paper, we present a deep-learning based framework which manages the uncertain user input and provides the user with a higher level control of the design process. The framework also imputes the input with missing information required by the computational algorithms. The approach starts by learning the probability distribution of possible linkage parameters with a deep generative modeling technique, called Variational Auto Encoder (VAE). This facilitates capturing salient features of the user input and relating them with possible linkage parameters. Then, input samples resembling the inferred salient features are generated and fed to the computational methods of kinematic synthesis. The framework post-processes the solutions and presents the concepts to the user along with a handle to visualize the variants of each concept. We define this approach as Variational Synthesis of Mechanisms. In addition, we also present an alternate End-to-End deep neural network architecture for Variational Synthesis of linkages. This End-to-End architecture is a Conditional-VAE (C-VAE), which approximates the conditional distribution of linkage parameters with respect to coupler trajectory distribution. The outcome is a probability distribution of kinematic linkages for an unknown coupler path or motion. This framework functions as a bridge between the current state of the art theoretical and computational kinematic methods and machine learning to enable designers to create practical mechanism design solutions.

Computational Creativity Via Assisted Variational Synthesis of Mechanisms Using Deep Generative Models

2019 ◽  
Vol 141 (12) ◽  
Author(s):  
Shrinath Deshpande ◽  
Anurag Purwar
Keyword(s):  
Probability Distribution ◽  
Computational Methods ◽  
Generative Models ◽  
Motion Generation ◽  
Kinematic Synthesis ◽  
User Input ◽  
Highly Nonlinear ◽  
Synthesis Of Mechanisms ◽  
End To End ◽  
Salient Features

Abstract Computational methods for kinematic synthesis of mechanisms for motion generation problems require input in the form of precision positions. Given the highly nonlinear nature of the problem, solutions to these methods are overly sensitive to the input—a small perturbation to even a single position of a given motion can change the topology and dimensions of the synthesized mechanisms drastically. Thus, the synthesis becomes a blind iterative process of maneuvering precision positions in the hope of finding good solutions. In this paper, we present a deep-learning-based framework which manages the uncertain user input and provides the user with a higher level control of the design process. The framework also imputes the input with missing information required by the computational algorithms. The approach starts by learning the probability distribution of possible linkage parameters with a deep generative modeling technique, called variational auto encoder (VAE). This facilitates capturing salient features of the user input and relating them with possible linkage parameters. Then, input samples resembling the inferred salient features are generated and fed to the computational methods of kinematic synthesis. The framework postprocesses the solutions and presents the concepts to the user along with a handle to visualize the variants of each concept. We define this approach as variational synthesis of mechanisms. In addition, we also present an alternate end-to-end deep neural network architecture for variational synthesis of linkages. This end-to-end architecture is a conditional-VAE, which approximates the conditional distribution of linkage parameters with respect to a coupler trajectory distribution. The outcome is a probability distribution of kinematic linkages for an unknown coupler path or motion. This framework functions as a bridge between the current state of the art theoretical and computational kinematic methods and machine learning to enable designers to create practical mechanism design solutions.

Kinematic Synthesis of Mechanisms and Robotic Manipulators With Binary Actuators

1995 ◽  
Vol 117 (4) ◽  
pp. 573-580 ◽  
Author(s):  
G. S. Chirikjian
Keyword(s):  
Finite Number ◽  
Low Cost ◽  
Robotic Manipulators ◽  
Kinematic Synthesis ◽  
Synthesis Of Mechanisms ◽  
Pick And Place ◽  
Discrete States ◽  
Binary Actuators ◽  
Pneumatic Cylinders ◽  
Very High

Binary actuators have only two discrete states (denoted “0” and “1”), both of which are stable without feedback. As a result, binary mechanisms and manipulators have a finite number of states. Major benefits of binary actuation are that extensive feedback control is not required, task repeatability can be very high, and two-state actuators are generally very inexpensive (e.g., solenoids, pneumatic cylinders, etc.), thus resulting in low cost robotic mechanisms. This paper develops algorithms for the optimal synthesis of binary manipulators and mechanisms for discrete tasks such as pick-and-place operations.

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