一种计算平面机构自由度的新方法_郭卫东.pdfVIP

49 7 Vol.49 No.7 2013 4 JOURNAL OF MECHANICAL ENGINEERING Apr. 2013 DOI 10.3901/JME.2013.07.125 * ( 100191) (Grübler-Kutzbach) Grübler-Kutzbach TH112 A New Method of Mobility Calculation for Planar Mechanisms GUO Weidong YU Jingjun (Robotics Institute, Beihang University, Beijing 100191) Abstract The classical Grübler-Kutzbach formula for calculating mobility of planar mechanisms seems very simple, however, it is not easy to obtain a correct result for some special mechanisms. In particular, by making an investigation of some cases existing in dozens of current-use textbooks relating to “Theory of Machines and Mechanisms” and “Fundamental to Machine Design”, it is found that some results derived from the well-known formula are not correct. For this reason, a new method of mobility calculation for planar mechanisms is proposed, which is establishing upon a derived Grübler-Kutzbach formula. In the proposed method and formula, the new concepts of real-constraint higher pair, redundant-constraint higher pair, full-constraint lower pair and half-constraint lower pair are introduced, thus the puzzle existing in the Grübler-Kutzbach formula can be solved effectively. The research is helpful for making the formula for calculating mobility of planar mechanisms more rigid and scientific. Key words Theory of machines and mechanisms Planar mechanisms Mobility Redundant constraints n=2 p =2 p =1 L H