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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]

It has long been a challenge to carry out the optimal design of parallel kinematic machine (PKM) simultaneously considering stiffness and mass performances. This paper proposes the stiffness and mass optimization of PKM by settling performance indices, constraint conditions based on parameter uncertainty and cooperative equilibrium among performances. Firstly, instantaneous energy-based stiffness indices and mass in motion are defined as objectives. Instead of computationally expensive numerical analysis, analytical mapping models between objectives and parameters are investigated to improve optimization efficiency. Then, considering the effects of parameter uncertainty resulted from manufacturing errors during construction, constraint conditions are formulated by probabilistic method. Based on particle swarm optimization (PSO), a multi-objective optimization is implemented. A group of solutions are obtained to flag as Pareto frontier that reflects the competitive features between stiffness and mass performances. A cooperative equilibrium searching method is proposed to find out the final solution. Finally, this optimization approach is exemplified and validated by a five degree-of-freedom (DoF) PKM. Although its mass increases 17.17%, the stiffness is nearly 3 times better than before optimization. [ABSTRACT FROM AUTHOR]

The crucial procedure of mobility and singularity identification of parallel mechanisms is widely recognized as how to determine their motions (constraints) concisely and visually. In this paper, we propose a geometric algebra (GA) based approach to determine the motions/constraints, mobility and singularity of parallel mechanisms mainly utilizing the geometric and algebraic relations. Firstly, the motions, constraints and their relations are represented by conformal geometric algebra (CGA) formulas in a concise form by employing the characterized geometric elements with G 4 , 1 . Secondly, the mobility of parallel mechanism, including its number and property and the axes of motions, not only at origin configuration but also in the prescribed workspace, is obtained by the procedure proposed in this paper. Thirdly, the singularity of parallel mechanism is identified by the two indices proposed in this paper with shuffle and outer products. Finally, a typical example is given to illustrate the motions/constraints, mobility and singularity analysis. This approach is beneficial to kinematic analysis and optimal design of parallel mechanisms, especially for which would be carried out in automatic and visual manner using computer programming languages. [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]

Parallel mechanisms (PMs) having three translational (T) and one rotational (R) movement capability draw continuous attention from academia and industry. The existing 3T1R PMs can only generate Schoenflies motion and bifurcation of Schoenflies motion. This paper proposes a new 3T1R motion that features one rotation about a varying axis plus three pure translations. Drawing mainly on finite screw theory, a hierarchical approach for type synthesis of limb structures of the PMs having 3T1R motion with variable rotational axis is presented by developing the basic limb bonds first and then their equivalent substitutions using the properties of screw triangle product. The assembly conditions for the PMs of this kind are discussed. Consequently, numerous novel PMs consisting of four identical limbs are synthesized using this technique. [ABSTRACT FROM AUTHOR]

It has been a desire to unify the models for structural and parametric analyses and design in the field of robotic mechanisms. This requires a mathematical tool that enables analytical description, formulation and operation possible for both finite and instantaneous motions. This paper presents a method to investigate the algebraic structures of finite screws represented in a quasi-vector form and instantaneous screws represented in a vector form. By revisiting algebraic operations of screw compositions, this paper examines associativity and derivative properties of the screw triangle product of finite screws and produces a vigorous proof that a derivative of a screw triangle product can be expressed as a linear combination of instantaneous screws. It is proved that the entire set of finite screws forms an algebraic structure as Lie group under the screw triangle product and its time derivative at the initial pose forms the corresponding Lie algebra under the screw cross product, allowing the algebraic structures of finite screws in quasi-vector form and instantaneous screws in vector form to be revealed. [ABSTRACT FROM AUTHOR]

This paper for the first time presents a finite screw approach to type synthesis of three-degree-of-freedom (DOF) translational parallel mechanisms (TPMs). Firstly, the finite motions of a rigid body, a TPM and its limbs are described by finite screws. Secondly, given the standard form of a limb with the specified DOF, the analytical expressions of the finite screw attributed to the limb are derived using the properties of screw triangle product, resulting in a full set of the 3-, 4- and 5-DOF limbs that can readily be used for determining all the potential topological structures of TPMs. Finally, the assembly conditions for type synthesis of TPMs are proposed by taking into account the inclusive relationship between the finite motions of a TPM and those of its limbs. The merit of this approach lies in that the limb structures can be formulated in a justifiable manner that naturally ensures the full cycle finite motion pattern specified to the moving platform. [ABSTRACT FROM AUTHOR]

Taking a horizontally-mounted 3-RPS parallel kinematic machine (PKM) as an example, this paper investigates passive and active gravity compensation strategies for improving PKM precision. Herein, R, P and S denote revolute, actuated prismatic and spherical joint, respectively. Based on inverse position kinematic and force analysis, passive gravity compensation is firstly implemented by three extension springs. Geometric parameters of these springs are optimized by minimizing potential energy fluctuation within a prescribed workspace. Then deformation caused by gravity is adopted to evaluate compensation strategies. The deviations of an end reference point demonstrate that passive gravity compensation is capable of substantially balancing gravity. In order to further eliminate the effect of gravity, active gravity compensation is proposed to adjust spring displacements by several one degree-of-freedom (DoF) translational mechanisms. Deformation of the 3-RPS PKM is directly regarded as the objective function for determining the active translations. Overall, both passive and active gravity compensations are able to improve mechanism precision due to the partial and complete gravity balancing capability, respectively, which makes the 3-RPS PKM suitable for the application of rough and fine machining. [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]

Driven by the requirements of inter-satellite link antenna for tracking mechanism with two degree-of-freedom (DoF), this paper proposes a 2-DoF over-constrained rotational parallel mechanism (RPM) with an articulated traveling platform and formulates its stiffness model considering gravitational effects. The stiffness modeling is implemented by three steps: 1) Considering the over-constrained property and gravitational effects, twist/wrench mapping models of two R (RU) 2 limbs connecting the fixed base and the articulated traveling platform are obtained based upon screw theory. 2) Employing deformation superposition principle, the compliance models of two R (RU) 2 limbs in their joint spaces are formulated, of which component compliance is described by n -DoF ( n ≤ 6) virtual springs; and 3) by applying deformation compatibility conditions and twist/wrench mapping models into the virtual work equations, the stiffness model of the 2-DoF over-constrained RPM considering gravitational effects is derived. From component, limbs to mechanism, the stiffness modeling process demonstrates their relations with clear physical meaning and unifies performances including kinematic, stiffness, accuracy and dynamics. This approach is verified by commercial FEA software. Finally the stiffness distribution and gravitational effects within prescribed workspace are discussed. [ABSTRACT FROM AUTHOR]

Presented in this paper is on the nonlinear dynamics of a planetary gear system with multiple clearances taken into account. A lateral–torsional coupled model is established with multiple backlashes, time-varying mesh stiffness, error excitation and sun-gear shaft compliance considered. The solutions are determined by using harmonic balance method from the equations in matrix form. The theoretical results from HBM are verified by using the numerical integration. Finally, effects of parameters are discussed. [Copyright &y& Elsevier]

• 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 type synthesis method for tensegrity robots is proposed. • The static stability criterion of the tensegrity unit is put forward. • The criterion of deformation stability is formulated based on a dynamic model. • An experiment is conducted to prove the effectiveness of the synthesis method. It is a tough task to figure out how to employ a small number of actuators to give a mobile robot multiple locomotion modes. This work suggested an unique type synthesis approach for tensegrity robots with few actuators and multi-locomotion mode by unit-splicing, focusing on robotic mechanisms and aiming at three locomotion modes that worms may realize (earthworm-like, inchworm, and tumbling locomotion). The static and deformation stability were used to screen out all of the tensegrity planar units that might achieve the desired locomotion modes. On this basis, traditional tensegrity structures are modified and springs are introduced in order to decrease the number of actuators. Then, all the tensegrity mechanisms that could be driven by two motors and realize the three locomotion modes were acquired by the splicing of units and merging of cables, and the value ranges of the parameters of robotic members that could satisfy the stability criteria were presented. Following the type synthesis results, a configuration was chosen, and a prototype was created. The experiment proved the viability of the type synthesis approach by demonstrating that the robot can implement the three locomotion modes with just two actuators. [ABSTRACT FROM AUTHOR]

• Topology characters are parameterized and identified by analytical expression • Algebraic mapping between performance with topology and dimension is constructed • Two algorithms are provided for topology generation and performance modeling • Synchronous optimal design for topologies and dimensions is carried out Parallel robots have attracted much attention from both academia and engineering in last two decades. For development of novel parallel robots, topology and dimensions are brought into sharper focus, which are associated closely and have coupled influence on both motion pattern and performance together. However, currently topology design and dimension design are always performed individually with independent aims, leading to local optimal solutions and difficulties in further modification. Actually, the intrinsic relationship between topology and performance is concerned far from abundant. In this article, a method for topology and dimension synchronous optimization is investigated by employing finite screw theory. Within this approach, two algorithms are formulated to parameterize and deliver topology characters in the same format with dimensions. Topology design and dimension design are converted into a synchronous optimization model with mixed variables and multi-objectives, resulting in global optimal solutions of both optimal topology and dimensions. Topology and dimension synchronous optimization of a kind of 1T2R parallel robots is presented and discussed by comparing with state-of-the-art methods. [ABSTRACT FROM AUTHOR]

• Six types of novel parallel machining robots are optimized. • A topology and layout integrated design approach is proposed. • The impact of topology and layout on performance and structure is discussed. The core components used in frontier fields typically have complex surface topography, difficult-to-remove workpiece materials, and extremely high machining quality and efficiency requirements. These characteristics pose major challenges to the performance of machining equipment. To address these issues, a class of six-limbs five degree of freedom (5-DOF) parallel machining robots with high stiffness and flexibility is designed. To cope with the coupling effect of multi-type parameters of robots on the optimal design, a comprehensive optimal design method combining mechanism theory and engineering experience is proposed. This method includes topology synthesis, layout evolution, performance design, and structure selection. Three performance indices, namely, stiffness, transmissibility, and mass, are considered. Two novel layouts and six novel prototypes have been optimized. Through the quantitative comparison and qualitative analysis of the above results, the influence of different layout and topology on the structure and performance of the robot is discussed, and several potential application scenarios are presented. The numerical simulation demonstrates that the designed six-limbed 5-DOF parallel robot exhibits satisfactory static behavior and flexibility, fulfilling the essential requirements for complex component machining. [ABSTRACT FROM AUTHOR]

• A class of 5-DoF parallel robots for in-situ machining is designed. • A topology and dimension synchronous design approach is proposed. • A novel full-size 5-DoF robot prototype is fabricated. Robotic machining has been successfully applied in thin-walled aluminum alloy components, but its ability to machine large steel components in-situ remains to be improved. To address this issue, a class of five-degree-of-freedom (5-DoF) parallel machining robots with high stiffness-mass ratio, easy installation, compact structure and reconfigurability is designed. To solve the problem of separation of topology and dimension designs, a topology and dimension synchronous optimization design method is proposed by parametric characterization and performance differential map of the robot. Three performance indices, namely, axial stiffness, feed stiffness, and mass are mainly considered. The influences of topology and layout on the performance are extensively investigated. We developed a full-size prototype according to the optimization results. Prototype data demonstrates that the 5-DoF parallel robot offers satisfactory static behavior, thereby fulfilling the essential requirements for the in-situ machining of large-scale steel components. Lastly, several in-situ machining robotic solutions are presented, thereby laying the foundation for other in-situ machining of large-scale steel components. [ABSTRACT FROM AUTHOR]

• An IDM of dimensional parameters and structural topology is proposed. • A machinability processing algorithm is developed to meet the manufacturability. • The stiffness obtained by the IDM is almost twice that of the PDM under the same mass. Dimensional parameters and structural topology have crucial impacts on the performance of robots. However, they are disjointed from each other in the design phase. To fill this gap, an integrated design method (IDM) of dimensional parameters and structural topology is proposed. The experiment is designed with dimensional parameters and mass retention ratio as variables. The topology optimization of components is implemented for minimum compliance. Then, a machinability processing algorithm is developed to make components satisfy the manufacturability. The stiffness matrix of each component is extracted by the finite element analysis (FEA) software, and the stiffness–mass metamodel is established by the response surface method (RSM). Finally, the performance models and optimization model are built, and the stiffness–mass metamodels are embedded in them. The optimization is conducted by particle swarm optimization (PSO) algorithm. A planar five-rotational joint (5R) parallel machining robot is considered to verify the effectiveness and superiority of the proposed method. Results indicate that the stiffness obtained by the proposed approach is approximately double that obtained by the parametric design method (PDM). [ABSTRACT FROM AUTHOR]

• A novel modular self-crossing mechanism is proposed. • Kinematic analysis of the self-crossing mechanism is conducted based on FIS theory. • Degree of freedom and gait of self-crossing locomotion is obtained. • Simulation is carried out to prove feasibility of self-crossing mechanism. In this paper, a novel mobile mechanism based on Bennett mechanism is proposed, which can realize self-crossing locomotion. Unlike the most of the self-crossing mechanisms, the proposed mechanism can be assembled modularly, which has better environment adaptability. Firstly, on the basis of revealing mechanism of the self-crossing movement, configuration of the self-crossing mechanism is designed. The mechanism consists of n Bennett mechanisms connected in series by 2(n -1) 3 R limbs that are symmetrically distributed on both sides of n Bennett mechanisms. Then, kinematic analysis of the mechanism is carried out based on finite and instantaneous screw theory, including mobility analysis and gait analysis. For the former, the number of degrees of freedom that the mechanism can achieve self-crossing locomotion is obtained, and for the latter, the trajectory of end point of the mechanism in the self-crossing movement is obtained. Finally, On the basis of theoretical analysis, simulation is conducted, and the results show that the proposed novel mechanism can realize self-crossing locomotion without interference, which verified the rationality of the mechanism. This paper provides a useful reference for the design and analysis of self-crossing mobile mechanism. [ABSTRACT FROM AUTHOR]

• A direct and analytical kinematic and force modeling method is applied. • Complete dynamic model of an over-constrained tracking mechanism is developed. • Practical dynamic identification is performed compromising precision and efficiency. • Predicted dynamic model for real-time control system is validated by experiments. To improve tracking precision against complex external forces in the working environment, dynamic model-based control algorithms are widely used in tracking mechanisms. As a foundation of the real-time dynamic control system, this paper focuses on the complete predicted dynamic modelling and dynamic parameter identification of a 2-DoF over-constrained tracking parallel mechanism. Firstly, the kinematic model is obtained by differential mapping of the topology models based on finite and instantaneous screws (FIS). Referred to virtual work principle, dynamic equation is constructed. To reduce the computation cost in practice, a linear model involving inertial and friction parameters is formulated for dynamic identification. A direct identification method is applied and all the parameters are obtained at the same time. Experiments are performed to show the accuracy and efficiency of the identification results. The contributions of the paper lie in 1) a concise method for constructing velocity and acceleration models of components is provided without tedious analysis 2) complete dynamic model of an over-constrained tracking parallel mechanism is developed 3) practical dynamic identification process is carried out compromising between precision and efficiency. [ABSTRACT FROM AUTHOR]