Design of Mechanisms to Draw Trigonometric Plane Curves

Yang, Liu; McCarthy, J. Michael

doi:10.1115/1.4035882

Cited by 7 publications

(8 citation statements)

References 19 publications

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“…Our use of cubic trigonometric Bezier curves follows the formulation of Han [17], who used four control points to define a curve that has the same properties as cubic polynomial Bezier curves [18]. Therefore, in this paper, we define a system of plane curves using cubic Bezier curve segments and then use the results of Liu and McCarthy [19] to design a mechanical system that draws the curves.…”

Section: Literature Reviewmentioning

confidence: 99%

“…Therefore, the component functions of a degree n Bezier curve are defined by a finite Fourier series in h, which means it is a trigonometric curve [15]. Liu and McCarthy [19] showed that a trigonometric curve p(h) defined by Fourier series is given by…”

Section: Degree N Bezier Curvementioning

confidence: 99%

“…Once each of the Bezier curves is written in the form of a trigonometric curve, we can use the results of Liu and McCarthy [19] to design the associated coupled serial chain. Expanding the powers of sine and writing the trigonometric Bezier curve in the form…”

Section: Compute the Coupled Serial Chainmentioning

confidence: 99%

“…Liu and McCarthy [19] showed how for each value k the coefficients a k and b k are used to compute the magnitudes, L k and M k , and phase angles w k and g k of vectors defining the links of the coupled serial chain…”

Section: Compute the Coupled Serial Chainmentioning

confidence: 99%

“…Fig. 3 The cursive letters that define Yang are defined by eight cubic Bezier curves listed in Table 2 (19) which means the maximum variation is less than 1% of the size of the curve. Figure 4 shows a comparison of these two curves.…”

Section: Linkage System To Draw Cursive Lettersmentioning

confidence: 99%

See 4 more Smart Citations

Design of a Linkage System to Write in Cursive

Liu

McCarthy

2017

Journal of Computing and Information Science in Engineering

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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.

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Section: Literature Reviewmentioning

confidence: 99%

Section: Degree N Bezier Curvementioning

confidence: 99%

Section: Compute the Coupled Serial Chainmentioning

confidence: 99%

Section: Compute the Coupled Serial Chainmentioning

confidence: 99%

Section: Linkage System To Draw Cursive Lettersmentioning

confidence: 99%

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Design of a Linkage System to Write in Cursive

Liu

McCarthy

2017

Journal of Computing and Information Science in Engineering

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Rolling Circles of Motions: Yesterday and Today

Tosun

Ersoy

2018

Models and Theories in Social Systems

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Exploratory design of mechanical devices with motion constraints

Roussel

Cani

Léon

et al. 2018

Computers & Graphics

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Mechanical devices are ubiquitous in our daily lives, and the motion they are able to transmit is often a critical part of their function. While digital fabrication devices facilitate their realization, motiondriven mechanism design remains a challenging task. We take drawing machines as a case study in exploratory design. Devices such as the Spirograph can generate intricate patterns from an assembly of simple mechanical elements. Trying to control and customize these patterns, however, is particularly hard, especially when the number of parts increases. We propose a novel constrained exploration method that enables a user to easily explore feasible drawings by directly indicating pattern preferences at different levels of control. The user starts by selecting a target pattern with the help of construction lines and rough sketching, and then finetunes it by prescribing geometric features of interest directly on the drawing. The designed pattern can then be directly realized with an easy-to-fabricate drawing machine. The key technical challenge is to facilitate the exploration of the high dimensional configuration space of such fabricable machines. To this end, we propose a novel method that dynamically reparameterizes the local configuration space and allows the user to move continuously between pattern variations, while preserving user-specified feature constraints. We tested our framework on several examples, conducted a user study, and fabricated a sample of the designed examples.

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Design of Mechanisms to Draw Trigonometric Plane Curves

Cited by 7 publications

References 19 publications

Design of a Linkage System to Write in Cursive

Design of a Linkage System to Write in Cursive

Rolling Circles of Motions: Yesterday and Today

Exploratory design of mechanical devices with motion constraints

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