Abstract
A homogeneous planar kinematic chain (KC) is a KC having all its constituting smallest independent circuits (fundamental circuits) of the same size. Davies [ J. Mech. 3, 87–100 (1968)] established, using graph theory, that a planar KC (homogeneous) of mobility M cannot have all fundamental circuits of size greater than M + 4. In the present paper many counterexamples to Davies's statement are presented and it is indicated that the maximum size of the circuits depends not only on the mobility of the mechanism but also on the number of links. The counterexamples given consist of, primarily, single degree of freedom (DOF) planar homogeneous KCs of loop sizes 6, 7 and 8; some zero DOF and tw DOF chains are also included. The causes for the failure of Davie's theorem have been analysed in detail to show that it is valid only in the domain of planar KCs with planar graphs.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
