## 1 Introduction
considered the influence of internal impact during configuration transformation, taking a controllable metamorphic patletizing robot as the research object, considering the multiple failure modes and the random and interval variables, and proposed a vibration reliability evaluation method during the configuration maintenance period after configuration transforming. However, the studies in references [43; 44] have focused more on the kinematic or dynamic reliability analysis of metamorphic mechanisms within each configuration maintaining period. Obviously, compared to configuration maintenance, the kinematic failure of switching between adjacent configurations is a more likely failure model for metamorphic mechanisms. Therefore, conducting reliability research on configuration switching has more theoretical and practical significance. Particularly for constrained metamorphic mechanisms, the transforming/maintenance of working configurations is mainly realized by the transforming/maintenance of the moving and static of the metamorphic kinematic joints (variable kinematic joints). Therefore, some specific \"switching\" structures of metamorphic joints need to be designed for realizing the transformation between moving and static. The inborn attribute of metamorphic joint determines that the failure of configuration transformation is the most frequent failure mode for the constrained metamorphic mechanism in completing operational tasks, and the ability of completing configuration transformation precisely is a crucial indicator for performance of the metamorphic mechanisms. Obviously, the reliability-based optimization design focusing on the stability of configuration transformation is the basis of improving the stability and reliability of configuration transformation. Currently, little literature is introduced about systematical research on the probability evaluation and the reliability-based optimization design of configuration transformation ability based on the force analysis during the kinematic status switch of metamorphic joints at the moment of configuration transformation. Based on the equivalent resistance gradient model, the study aims to establish a probability evaluation model of the configuration transformation ability of the constrained metamorphic mechanism, and propose a reliability optimization design method aiming at obtaining a high probability of repeated implementation ability of configuration transformation, which provides a theoretical basis and an effective design basis for promoting the engineering application of constrained metamorphic mechanisms. The remainder of the paper is organized as follows: Section 2 introduces the working process and structure composition principle of constrained metamorphic mechanisms. Section 3 proposes modularized force analysis methods of constrained metamorphic mechanisms first and then completes the structural design for a novel metamorphic revolute joint according to force analysis. Section 4 establishes the evaluation model of configuration transformation ability of constrained metamorphic mechanism under deterministic parameters and then presents a probabilistic evaluation model of configuration transformation ability by considering the randomness of input errors in practical application. Section 5 proposes a reliability-based optimization design method of constrained metamorphic mechanisms oriented to the stability of configuration transformation. In Section 6, the proposed method of reliability optimization design is illustrated by an example of the paper folding metamorphic mechanism to verify its feasibility and effectiveness. Finally, a discussion is presented in Section 7, and Section 8 concludes the paper. General Metamorphic Working Process and Structure Composition Principle of Constrained Metamorphic Mechanisms