TAILIEUCHUNG - Advances in Robot Kinematics - Jadran Lenarcic and Bernard Roth (Eds) Part 5

Tham khảo tài liệu 'advances in robot kinematics - jadran lenarcic and bernard roth (eds) part 5', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 114 Z. Luo and . Dai can only find feasible linkages with a large number of links. As Hunt stated in Chapter 4 of his book Hunt 1978 Yet neither Kempe nor anyone else since has established a method for isolating the best or the simplest linkage for tracing a particular curve. In the history all feasible linkages with a small number of links for algebraic curves generation were invented by some great masters using their geometrical intuitions Please see the Appendix for details . Nevertheless geometrical intuitions are difficult to be duplicated and they may not guarantee all solutions for a synthesis problem be found. The above investigation raises a question Are there any undiscovered 6-bar linkages for straight-line generation This paper proposes a numerical approach to attack the problem. Note that it is possible to extend the approach for nding spatial 6R single loop overconstrained mechanisms see remarks at the end of Section . 2. Searching for 6-bar Straight-line Linkages Figure 1. Six arrangements of 6-bar linkages for a path generation with the asterisk denoting the position of coupler-point. Figure 1 illustrates 6 possible arrangements of 6-bar linkages for straightline generation. As can be seen from Fig. 4 that the existing straight-line 6-bar linkages are either Watt-I1 linkages or Stephenson-I linkages. Indeed based on the principle of inversion and Robert s cognate theorem we can conclude that Stephenson-II2 linkages and Stephenson-III linkages cannot generate a straight-line. Other arrangements should be 1This is still an open problem. Smith 1998 tried to prove it but failed. 2 According to Artobolevskii 1964 Alekseyev 1939 discovered the dimensional relationships of the generalized linkage on 1939 but the authors are not able to find Alekseyev s proof while the short proof given in Artobolevskii s book is indeed invalid. Searching for Undiscovered Planar Straight-line Linkages 115 examined individually. Synthesizing straight-line linkages is

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