Kinematic Analysis for the Spatial Interlocking 3-UU Mechanism With the Wide Range of Motion

Abstract

Mechanisms that balance wide range of motion(ROM) with increased stiffness are gradually gaining attention in robotic applications. This letter proposed kinematic methods for the spatial interlocking 3-UU mechanism based on Lie Group, which consists of a fixed base and a moving platform connected by three serial limbs. A previous mathematical mobility analysis confirms that the mechanism has 0 degrees of freedom (DoFs), and the prototypes demonstrate unexpected large platform motions. Since the 3-UU mechanism theoretically has zero DoFs, existing serial and parallel kinematic methods cannot determine its motion. This study addresses this seeming contradiction. We propose a kinematic method based on the renowned Baker-Campbell-Hausdorff formula in Lie Group. Upon optimization, the positional error is limited to a maximum of 0.71 mm at a 250 mm length within an actuated joint motion range of 30 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^{\circ }$</tex-math></inline-formula> (-15 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^{\circ }$</tex-math></inline-formula> to 15 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^{\circ }$</tex-math></inline-formula> ). This result represents a significant step in addressing the unexplored domain of the kinematic method of 3-UU mechanisms and promoting the widespread application of the mechanism.