Synthesis of scaling mechanisms for geometric figures with angulated-straight elements

Angulated-straight element is proposed by combining pantograph element and Hoberman element. It is prepared to construct scaling mechanisms for geometric figures. Angulated-straight element is a kind of scissor-like element that moves along a fixed angle in radial direction, coined radial-scaling element. To explore the advantages of this new element, scaling characteristics of the radial-scaling element are proposed, such as configurations, kinematic characteristics and scaling ratio. Scaling characteristics of hybrid-radial-scaling element are also investigated to enlarge the scaling ratio of radial-scaling element. All configurations of angulated-straight element are synthesized by a rotation method presented in this article. The kinematic characteristics and scaling ratios are analyzed and compared between angulated-straight element and Hoberman element. Synthesis methods of scaling mechanisms for geometric figures are presented by combining the geometric characteristics and design parameters of regular polygon and regular polyhedron. The result shows that shapes and combinations of linkages determine the scaling characteristics of the radial-scaling element. Scaling characteristics analysis of scaling elements is a useful basic theory for choosing and constructing scaling mechanisms. Types of scaling mechanism are enriched. These scaling mechanisms have a certain value of application.