A method for optimizing the shape, posture and arrangement of sipes based on parametric design factors was developed to improve the grip performance of winter tyres. This is a method that involves repeatedly conducting friction coefficient measurement experiments on a group of 3D-printed models made of materials with physical properties equivalent to tyre rubber, and Bayesian optimization of multiple parameter combinations that are expected to enhance performance. First, the effectiveness of this method was verified by evaluating the step-by-step improvement in grip performance with each iteration of the Bayesian optimization loop. Furthermore, we attempted to improve grip performance on the newly emerged ‘Twist sipe’ design created by expanding the design space while confirming the effectiveness of this method. Finally, the discussion revolved around the type and selection of acquisition functions necessary for acquiring a Gaussian process regression model that will be used in selecting the combination of design factors for the next loop in Bayesian optimization.

Prime structures are link chains with 0 DoF (degrees of freedom), not including subchains with 0 or fewer DoF, which are expected to be used in systematic kinematic analyses and design of link mechanisms. This paper describes the motion analysis of link chains induced from spatial prime structures. For all 3-link spatial prime structures, namely, RCS, PCS, RSS, PSS and CCC prime structures, and a 4-link spatial prime structure with a single kinematic loop, kinematic analysis methods are established. Displacements, velocities and accelerations of link chains, which are induced from prime structures by removing one link, are derived. More than one link chain is induced from a prime structure, but if an analysis method is developed for one link chain, others can be easily analyzed using coordinate transformation. In the displacement analysis, we derive algebraic solutions as possible, and for the rest, we develop a method to find all solutions, including complex solutions as solutions for a higher-order algebraic equation. Displacement of a multi-loop prime structures is also analyzed with combination of analyses of several single-loop prime structures. For an example of the application of prime structures, the motion of a spatial RCS-R-PSS 6-link mechanism with 1 DoF is analyzed. It was confirmed that the proposed analyses were correct and effective because the results with the proposed analyses completely agreed with those obtained from CAD software.