scholarly journals Design of a Linkage System to Write in Cursive

2017 ◽  
Vol 17 (3) ◽  
Author(s):  
Yang Liu ◽  
J. Michael McCarthy
Keyword(s):  
Mechanical System ◽  
Complex Plane ◽  
Design Methodology ◽  
Plane Curves ◽  
Chinese Characters ◽  
Bezier Curves ◽  
Bézier Curves ◽  
Cursive Handwriting ◽  
Serial Chain ◽  
Serial Chains

This paper presents a design methodology for a system of linkages that can trace planar Bezier curves that represent cursive handwriting of the alphabet and Chinese characters. This paper shows that the standard degree n Bezier curve can be reparameterized so that it takes the form of a trigonometric curve that can be drawn by a one degree-of-freedom coupled serial chain consisting of 2n links. A series of cubic Bezier curves that define a handwritten name yields a series of six-link coupled serial chains that trace these curves. We then show how to simplify this system using cubic trigonometric Bezier curves to obtain a series of four-link serial chains that approximate the system of Bezier curves. The result is a methodology for the design of a mechanical system that draws complex plane curves such as the cursive alphabet and Chinese characters.

Design of Mechanisms to Draw Trigonometric Plane Curves

2017 ◽  
Vol 9 (2) ◽  
Author(s):  
Yang Liu ◽  
J. Michael McCarthy
Keyword(s):  
Fourier Transform ◽  
Design Methodology ◽  
Plane Curve ◽  
Plane Curves ◽  
Trigonometric Functions ◽  
The Third ◽  
Universality Theorem ◽  
Serial Chain ◽  
Cable Drive ◽  
Serial Chains

This paper describes a mechanism design methodology that draws plane curves which have finite Fourier series parameterizations, known as trigonometric curves. We present three ways to use the coefficients of this parameterization to construct a mechanical system that draws the curve. One uses Scotch yoke mechanisms for each of the terms in the coordinate trigonometric functions, which are then added using a belt or cable drive. The second approach uses two-coupled serial chains obtained from the coordinate trigonometric functions. The third approach combines the coordinate trigonometric functions to define a single-coupled serial chain that draws the plane curve. This work is a version of Kempe's universality theorem that demonstrates that every plane trigonometric curve has a linkage which draws the curve. Several examples illustrate the method including the use of boundary points and the discrete Fourier transform to define the trigonometric curve.

Design of Mechanisms to Trace Plane Curves

2016 ◽  
Author(s):  
Yang Liu ◽  
J. Michael McCarthy
Keyword(s):  
Fourier Series ◽  
Algebraic Curve ◽  
Design Methodology ◽  
Plane Curve ◽  
Plane Curves ◽  
The Third ◽  
Universality Theorem ◽  
Serial Chain ◽  
Plane Algebraic Curve ◽  
Trace Curves

This paper describes a mechanism design methodology that assembles standard components to trace plane curves that have a Fourier series parameterization. This approach can be used to approximate complex plane curves to interpolate image boundaries constructed from points. We describe three ways to construct a mechanism that generates a curve from a Fourier series parameterization. One uses Scotch yoke linkages for each term of Fourier series which are added using a belt drive. The second approach uses a coupled serial chain for each coordinate Fourier parameterization. The third method uses one constrained coupled serial chain to trace a specified plane curve. This work can be viewed as a version of the Kempe Universality Theorem that states that a linkage exists that can trace any plane algebraic curve. In our case, we include belts and pulleys, and obtain linkages that trace curves that have Fourier parameterizations.

Quadratic Bezier Curves for Multi-Agent Coordinated Arrival in the Presence of Obstacles

2021 ◽  
Author(s):  
Satyanarayana G. Manyam ◽  
David Casbeer ◽  
Isaac E. Weintraub ◽  
Dzung M. Tran ◽  
Justin M. Bradley ◽  
...  
Keyword(s):  
Bezier Curves ◽  
Bézier Curves ◽  
Multi Agent

Curves used in highway design and Bezier curves

2021 ◽  
Vol Accepted ◽  
Author(s):  
Bayram Şahin ◽  
Aslı Ayar
Keyword(s):  
Bezier Curves ◽  
Bézier Curves ◽  
Highway Design

scholarly journals A new method on motion planning for mobile robots using jump point search and Bezier curves

2021 ◽  
Vol 18 (4) ◽  
pp. 172988142110192
Author(s):  
Ben Zhang ◽  
Denglin Zhu
Keyword(s):  
Motion Planning ◽  
Initial Point ◽  
Target Point ◽  
Jump Point ◽  
Bezier Curves ◽  
Bézier Curves ◽  
Front End ◽  
Planning Algorithm ◽  
Point Search ◽  
Path Planning Algorithm

Innovative applications in rapidly evolving domains such as robotic navigation and autonomous (driverless) vehicles rely on motion planning systems that meet the shortest path and obstacle avoidance requirements. This article proposes a novel path planning algorithm based on jump point search and Bezier curves. The proposed algorithm consists of two main steps. In the front end, the improved heuristic function based on distance and direction is used to reduce the cost, and the redundant turning points are trimmed. In the back end, a novel trajectory generation method based on Bezier curves and a straight line is proposed. Our experimental results indicate that the proposed algorithm provides a complete motion planning solution from the front end to the back end, which can realize an optimal trajectory from the initial point to the target point used for robot navigation.

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