Movable Planar 6T9R Mechanisms

• Main Authors: Jeng-Hiung Lee, 李正雄
• Other Authors: Chung-Ching Lee
• Format: Others
• Language: zh-TW
• Published: 2006
• Online Access: http://ndltd.ncl.edu.tw/handle/24400835399429141487

碩士 === 國立高雄應用科技大學 === 模具工程系碩士班 === 94 === Based on the structural type of six ternary links and nine revolute pairs (abbreviated as 6T9R) derived from the commercialized triangular expandable toy and two key-ring ornaments, the mobility of the generalized planar 6T9R mechanism is studied in this thesis. According to Grubler criterion, the degree of freedom of this kind of mechanism is -3 and it should not have constrained motion. However, due to the special geometric and dimensional constraints, some of such mechanisms can still have constrained motion. In order to enable the planar 6T9R mechanisms to be characterized by the constrained motion, the purpose of this thesis is focused on finding new movable overconstrained mechanisms coming from link dimensions and geometric relations. Firstly, the geometric structure of a general planar 6T9R mechanism is sketched and its topological structure is analyzed. Then, by applying the vector-loop approach to set up input-output displacement equation of the fourbar loop, we further develop vector-loop displacement equations of the general planar 6T9R mechanism and derive six groups of loop displacement equations. Utilizing these derived equations and with the help of symbolic program － Mathematica, we identify the mobility criteria of the general planar 6T9R mechanism through the linear dependent relation, direct elimination method and symmetrical function elimination technique respectively. As a result of the findings of this work, we know that if the 6T9R mechanism is movable with constrained motion, some restriction on link dimensions must be taken based on the mobility criteria derived in this thesis。 Finally, proceeding with the above criteria, we have synthesized one kind of novel 6T9R mechanism that has constrained motion. Furthermore, AutoCAD and Working Model 2D software are used to confirm and simulate the motion of this new 6T9R mechanism. In the meantime, the mobility and motion displacement relations of the commercialized triangular expandable toy and the key ornament mechanisms are made and simulated too..