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• A design method of parallel flexible mechanisms is proposed. • Principles of stiffness superposition and joint type determination are deduced. • A design example of the RCC and the final structure are presented. Parallel flexible mechanisms with joints can better avoid stress concentration and achieve large motion range compared with integrated-structure ones. However, because of the lack of a mathematical model that can describe the stiffness contribution from the joints to the whole mechanism, the mechanism design is difficult and needs to be addressed. This paper proposes a synchronous design method involving stiffness and topology for parallel flexible mechanisms. To introduce and explain this method, this paper deduces two fundamental principles, namely, "Linear Stiffness Superposition Principle (LSSP)" and "Joint Type Determination Principle (JTDP)", and their deduction processes serve as the cores of the design method. To verify the method's effectiveness, a design process of a Remote Central Compliance (RCC) is presented as an example. [ABSTRACT FROM AUTHOR]

• This paper proposes a structure of a planar three-limb flexible mechanism. • The determination of equilibrium and stability by contour maps is introduced. • The variation of the multi-stability topology of the mechanism is analyzed. In general, the classical multi-stable mechanisms are made of single-loop bi-stable mechanism elements, but this paper proposes a novel structure of a planar three-limb flexible mechanism whose multi-stability is dependent on the structure parameters. The structure of this flexible mechanism is ingeniously designed to have a large selection range of the original limb length, resulting in the variation of the multi-stability distribution and the possible switching paths. To analyze the variation of this flexible mechanism, the paper introduces a method avoiding computational singularity to determine the stability by contour map and a method to draw the multi-stability topology to seek for the possible switching paths. Using these methods, the paper presents the variation of the multi-stability topology of an axisymmetric and two mirror-symmetric planar three-limb flexible mechanisms as the original length of the limbs increases. The results shows the mulita-stability of this flexible mechanism can be determined by the original length of the limbs and limb arrangement. The whole statements provide a theoretical basis for designing and applying such type of flexible multi-stable mechanism. [ABSTRACT FROM AUTHOR]