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• A SPMM with eight stable equilibrium states is proposed. • The kinetostatic model and the multi-stability topologies of SPMM are developed. • The stabilities and switching paths are verified by experiments. A multi-stable flexible mechanism is a mechanical device that can switch to different stable equilibrium states under external power. Most existing multi-stable mechanisms are achieved by splicing bi-stable mechanisms. This paper proposes a novel Spatial Parallel Multi-stable Mechanism (SPMM) without bi-stable mechanisms connected, which even could achieve eight stable equilibrium states and meanwhile contain bi-stable mechanisms' advantages such like simple structure and reliable abilities. To identify the equilibrium states, the paper develops a kinetostatic model using the Energy-Kinematics Differential Equations (EKDE) for the proposed SPMM. Based on the equilibrium states, the multi-stability topologies are drawn referring to direct groups, including the distribution of various equilibrium states and the switching paths between every two stable states. At last, the paper shows the experimental results of a 3D printed prototype and verify the eight-stability behaviors and the switching paths through unstable equilibrium states. A concept of the application in deformable cable protection shell using the SPMM is introduced. [ABSTRACT FROM AUTHOR]

• 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]

• A calculation method of the force space for coupling-input CDPRs is proposed. • The boundary equations of the force space are derived. • The Chebyshev center of the force space is analyzed. • Two load capacity indices are proposed to optimize a coupling-input CDPR. CDPRs (cable-driven parallel robots) with passive limbs are characterized by simplicity of construction and ease of control due to the reduction in the number of cables. However, the limited carrying capacity of passive limbs containing springs has an important impact on the load capacity of CDPRs. To design a CDPR with a good load capacity, an optimization design based on the force space index is carried out in this paper. First, we present an accurate calculation method of the force space for coupling-input CDPRs with passive limbs and derive the force space boundary equations. Subsequently, the Chebyshev center of the force space is defined, and its calculation method is presented. Then, we establish two load-capacity indices to optimize the design parameters of a 3-DOF (degree of freedom) coupling-input CDPR. Finally, it is shown that the isotropic load capacity of a 3-DOF coupling-input CDPR is better when Chebyshev center of the force space is closer to the force origin (origin of the force coordinate system). [ABSTRACT FROM AUTHOR]

• A tensegrity leg combining tensegrity structure with rigid mechanism is developed. • Force-workspace is proposed to reveal the unique force characteristics of legs. • A tensegrity quadruped robot is found to have a large load-weight ratio. • A tensegrity quadruped robot can adapt to terrains by dynamic-morphology ability. Tensegrity robots, which are famous for their lightweight and capability of sustaining massive loads, have unique potential applications in task execution in complex environments. In this paper, a quadruped robot with tensegrity legs is proposed. By combining the tensegrity structure with a rigid mechanism, a 3-DOF tensegrity leg is developed. Necessary theoretical basis of the tensegrity leg including kinematics, statics, force space and force-workspace have been derived and proposed for design and control. A quadruped prototype based on tensegrity legs is manufactured and shows unique walking ability in different morphologies. The high load performance and terrain adaptability based on dynamic morphologies of the quadruped robot is verified by experiments. [ABSTRACT FROM AUTHOR]

• A new type of tensegrity robot (FTR) based on new class 1 tensegrity system is proposed. • The kinematic and static problems of FTRs are analyzed using the law of minimum energy. • The force space is proposed to present the relationship between external and internal forces acting on the FTR. Tensegrity robots, which are famous for their light weight and high adaptability, have unique potential applications in space exploration and task execution in complex environments. In this paper, a new type of tensegrity robot containing springs is introduced and analysed. The kinematic and static problems of the tensegrity robot are solved using the law of minimum energy. The accessible workspace of the tensegrity robot is calculated using a numerical method according to the kinematic and static model. In addition, the feasible force space, which is the collection of external forces that can be applied to the tensegrity robot in a certain equilibrium configuration, is derived and verified using a particular tensegrity robot as an example. [ABSTRACT FROM AUTHOR]