Computer-Aided Design 44 (2012) 1141–1150 Contents lists available at SciVerse ScienceDirect Computer-Aided Design journal homepage: www.elsevier.com/locate/cad A hybrid computer-aided linkage design system for tracing open and closed planar curves Cong Yue a , Hai-Jun Su a,b,∗ , Q.J. Ge c a Department of Mechanical Engineering, University of Maryland Baltimore County, Baltimore, MD 21250, USA b Department of Mechanical and Aerospace Engineering, Ohio State University, Columbus, OH 43210, USA c Department of Mechanical Engineering, Stony Brook University, NY 11794, USA article info Article history: Received 9 November 2011 Accepted 9 June 2012 Keywords: Linkage design Path generation Planar curves Fourier descriptors Computer-aided mechanism design abstract This paper presents a computer-aided linkage design system for tracing prescribed open or closed planar curves. The mechanism design is considered a mixture of science and art. The former is about utilizing computers to rigorously size a mechanism in meeting a set of design requirements and the latter is about taking advantage of designers’ experience to narrow down the design domain and speed up the design process. The ultimate goal of the presented design system is to incorporate both science and art into the linkage design process by (1) developing an automatic design framework that is based on library searching and optimization techniques and (2) developing an interactive design framework that is based on advanced human–computer interfaces. To enable the design automation framework, we first pre- built a library of open and closed planar curves generated by commonly used planar linkages. We then turned the classical linkage path generation problem into a library searching problem together with a local optimization problem. To enable the interactive design framework, we developed a set of design interfaces that facilitate designers to intervene and steer the design process. This hybrid design system was developed based on our existing VRMDS (Virtual Reality Mechanism Design Studio) framework. To demonstrate its functionalities, we provided four representative design cases of 4-bar and crank-slider linkages. The result shows that the system returned a desired solution in seconds. We also demonstrate the extensibility of the system by implementing designs of planar 4-bar and crank-slider linkages. © 2012 Elsevier Ltd. All rights reserved. 1. Introduction Mechanical linkage is an assembly of links that are connected together by kinematic pairs or joints to transform forces and movement [1,2]. There is a long history of applying computers to linkage design and numerous related software systems have been developed by both academia and industry. Linkage design software like LINCAGES [3,4], Sphinx [5], SPADES [6] and Synthetica [7] focus on dimensional synthesis of special types of linkages. LINCAGES mainly concentrates on 4-bar or 6-bar planar and spherical linkages. Sphinx solves the motion generation problem on linkages with four revolute joints while SPADES on spatial linkage with four cylindrical joints. Synthetica only considers spatial linkage with serial chains. Furthermore, all the software mentioned above are all designed to be as automatic as possible; they are all lacking in functionalities that allow interaction between computers and ∗ Corresponding author at: Department of Mechanical and Aerospace Engineer- ing, The Ohio State University, Columbus, OH 43210, USA. Tel.: +1 6142922239; fax: +1 6142923163. E-mail address: su.298@osu.edu (H.-J. Su). designers, hence the designer’s experience needs to be fully exploited in the design process. Commercial linkage design systems including WATT [8] by Heron Technologies Inc., SyMech [9] by SyMech Inc. and Ch Mechanism Toolkit by SoftIntegration Inc. [10] provide some interactive design elements that allow designers to specify different functionalities for the desired linkage. Unfortunately, these tools still have to focus on one or two types of linkages, and none of them provide a full dynamic simulation for general mechanisms. See [11] for a comprehensive list of applications for computer-aided mechanism design. On the other hand, general commercial CAD software such as Pro/ENGINEER, CATIA, AutoCAD and SolidWorks all provide geometric constraint solvers that have been used for linkage design [12]. The built-in constraint solver is a black-box solver which provides little information about the design problem hence prevent them from redeeming the design process when the solver failed. Also they are limited to path generation problems with precision points. Extra design requirements would be hard to be integrated into the solution process. MATLAB’s SimMechanics toolbox also provides a powerful multi-body dynamics solver. However, its building process is based on block diagrams. 0010-4485/$ – see front matter © 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.cad.2012.06.004