Multi-Bifurcation and Environmental Adaptability of a Novel Line-Symmetric Double-Centered Metamorphic Mechanism

Abstract

To improve the environmental adaptability of the mechanism, this letter proposes a metamorphic mechanism configuration synthesis method based on environmental constraint characteristics. In particular, a novel 6R line-symmetric double-centered metamorphic mechanism is synthesized and the multi-bifurcation characteristics and environmental adaptability are analyzed and verified. Firstly, a configuration synthesis method is proposed based on the bifocal geometric constraints of the elliptical oblique section of the pipe. The variation of the instantaneous mobility with the number of links is derived and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</i>=<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i>=3 is the minimum number of links that the mechanism is movable. Then, for the 6R mechanism, the joint velocity solution spaces of all the motion branches are revealed through the closed-loop and higher-order kinematics. Further, the correlation between the joint angle, configuration, and environment layers is demonstrated. The results show that the 6R mechanism has four motion branches (<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">MB</i><inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$_{1}$</tex-math></inline-formula>, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">MB</i><inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$_{2}$</tex-math></inline-formula>, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">MB</i><inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$_{3}$</tex-math></inline-formula>, and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">MB</i><inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$_{4}$</tex-math></inline-formula>) with different topological structures corresponding to different pipe environments and four 4R serial motion branches (<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">SMB</i><inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$_{1}$</tex-math></inline-formula>, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">SMB</i><inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$_{2}$</tex-math></inline-formula>, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">SMB</i><inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$_{3}$</tex-math></inline-formula>, and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">SMB</i><inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$_{4}$</tex-math></inline-formula>). Eventually, a wheeled metamorphic robot is designed, and the controllable motion branch transformation of the 6R mechanism and the pipe environment adaptability of the robot are proved by prototype experiments.