Geometric and kinematic analysis of a seven-bar three-fixed-pivoted compound-joint mechanism Guowu Wei, Jian S. Dai * Department of Mechanical Engineering, King’s College London, University of London, Strand, London WC2R 2LS, UK article info Article history: Received 7 October 2008 Received in revised form 19 April 2009 Accepted 18 May 2009 Available online 23 October 2009 Keywords: Three-fixed-pivoted Classification Kinematics Workspace Singularity Isotropy abstract This paper investigates a seven-bar three-fixed-pivoted compound-joint mechanism and presents a systematic classification based on the rotatability criterion of its various types evolved from the change of link parameters. By decomposing the mechanism into two closed loops that provide respectively position and orientation of the end-effector link, closed form kinematic equations are developed using two four-bar analytical equations in sequence for geometric analysis of the mechanism. The paper further derives the Jaco- bian matrices of the mechanism and presents its kinematic analysis. In the extended group of this mechanism, the paper investigates four typical mechanisms, examines their work- spaces and singularity based on the Jacobian matrices and implements the condition num- ber analysis to identify the isotropy distribution. Ó 2009 Elsevier Ltd. All rights reserved. 1. Introduction Interest in using closed-loop linkages as robotic manipulators has arisen in the past two decades. Closed-loop manipula- tors offer advantages of eliminating gear trains and facilitating other drive transmissions that are usually demanded in open- loop manipulators. Applying closed-loop planar linkages, particularly the two-dof closed-loop planar linkages to robotic field began from late 1980s. In 1985, Asada and Ro [1] introduced the direct drive to a two-dof five-bar compound-joint planar mechanism to overcome the problem faced by the open-loop mechanism. In 1986, Bajpai and Roth [2] analyzed the influence of the link lengths on the reachable workspace of the same two-dof five-bar manipulator whose classification and effect of orientation of the wrist on the floating link were further presented by Ting [3] in 1992. Since 1990s, more two-dof five-bar planar linkages were proposed and their geometry and kinematics were examined [4– 8]. Further to these mechanisms, the seven-bar mechanism as a type of two-dof planar mechanisms started drawing atten- tion from the mechanism and robotics community. In 1996, Gosselin [9] developed a seven-bar linkage by adding a crank to the Watt II six-bar linkage to form a three-legged planar parallel mechanism with one ternary link as its platform and ana- lyzed its kinematics and static characteristics. Using Assur group, Innocenti [10,11] presented the position analysis [12,13] for synthesis of a three-looped Assur seven-bar mechanism with respect to its assembly configurations. Type synthesis of a two-dof seven-bar planar mechanism with fixed-pivoted single joints was carried out by Fang and Zou [14] that reveals four types of linkages. Further to this, Balli and Chand [15] proposed a synthesis method of a three-pivoted planar seven-bar mechanism using dead-center positions with variable topology analysis to reduce the solution space. In 2003, a two-dof 0094-114X/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.mechmachtheory.2009.05.009 * Corresponding author. E-mail address: Jian.dai@kcl.ac.uk (J.S. Dai). URL: http://www.kcl.ac.uk/schools/pse/diveng/research/cmms/jsd/ (J.S. Dai). Mechanism and Machine Theory 45 (2010) 170–184 Contents lists available at ScienceDirect Mechanism and Machine Theory journal homepage: www.elsevier.com/locate/mechmt