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To analyze the quantitative mapping relationship between the geometric errors of the five-axis CNC machine tool and the tooth surface deviation of spiral bevel gears, and identify the key geometric errors that affect the machining deviation of the spiral bevel gear tooth surface, a sensitivity analysis method for tooth surface machining deviation of spiral bevel gear based on screw theory and EFAST method is proposed. Firstly, the machining model of the spiral bevel gear tooth surface based on the five-axis CNC machine tool is established. Then, the geometric error transfer model of the machine tool is established based on the screw theory. Combined with the EFAST global sensitivity analysis method, the key geometric errors that affect tooth surface deviation are identified. Finally, the reliability and effectiveness tests are performed by comparing the results to the local sensitivity analysis method and simulating compensation for the key geometric errors. The result of compensation shows that the tooth surface deviation is reduced significantly according to global sensitivity analysis. The feasibility of applying sensitivity analysis to control the tooth surface deviation of spiral bevel gears has been demonstrated. [ABSTRACT FROM AUTHOR]

Kinematics is a hot topic in robotic research, serving as a foundational step in the synthesis and analysis of robots. Forward kinematics and inverse kinematics are the prerequisite and foundation for motion control, trajectory planning, dynamic simulation, and precision guarantee of robotic manipulators. Both of them depend on the displacement models. Compared with the previous work, finite screw is proven to be the simplest and nonredundant mathematical tool for displacement description. Thus, it is used for displacement modelling of serial robots in this paper. Firstly, a finite-screw-based method for formulating displacement model is proposed, which is applicable for any serial robot. Secondly, the procedures for forward and inverse kinematics by solving the formulated displacement equation are discussed. Then, two typical serial robots with three translations and two rotations are taken as examples to illustrate the proposed method. Finally, through Matlab simulation, the obtained analytical expressions of kinematics are verified. The main contribution of the proposed method is that finite-screw-based displacement model is highly related with instantaneous-screw-based kinematic and dynamic models, providing an integrated modelling and analysis methodology for robotic mechanisms. [ABSTRACT FROM AUTHOR]

The cellular space robot (CSR) is a new type of self-reconfigurable robot. It can adapt the variety of on-orbit service tasks with large space spans through multi-level reconfiguration mechanisms. As the CSR has a large configuration space, kinematic solving becomes a key problem affecting on-orbit operation capability, and kinematic automatic solving research must be conducted. In order to solve this problem, firstly, the cellular space robot system capable of realizing multi-level self-reconfiguration is proposed for the demand of space on-orbit service, and the kinematic equations of modules are constructed by considering a single module function using screw theory. Secondly, the kinematics of the cellular space robot are encapsulated and divided into multiple levels, and the multilevel-assembly relationship-description method for robotic systems is proposed based on graph theory. On this basis, the pathway-solving algorithm is proposed to express the robot organization reachability information. Finally, the module–organ–robot multilevel kinematics solving algorithm is proposed in combination with screw theory. In order to verify the effectiveness of the algorithm in this paper, numerical simulation is used to compare with the proposed algorithm. The results show that compared with the traditional algorithm, the method in this paper only needs to update part of the assembly relations after organ migration, which simplifies the kinematic modeling operation and improves the efficiency of kinematic computation. [ABSTRACT FROM AUTHOR]

The seven-degree-of-freedom space manipulator, characterized by its redundant and aspheric wrist structure, is extensively used in space missions due to its exceptional dexterity and multi-joint capabilities. However, the non-spherical wrist structure presents challenges in solving inverse kinematics, as it cannot decouple joints using the Pieper criterion, unlike spherical wrist structures. To address this issue, this paper presents a closed-form analytical method for solving the inverse kinematics of seven-degree-of-freedom aspheric wrist space manipulators. The method begins by identifying the redundant joint through comparing the volumes of the workspace with different joints fixed. The redundant joint angle is then treated as a parametric joint angle, enabling the derivation of closed-form expressions for the non-parametric joint angles using screw theory. The optimal solution branch is identified through a comparative analysis of various self-motion manifold branches. Additionally, a hybrid approach, combining analytical and numerical methods, is proposed to optimize the parametric joint angle for a trajectory tracking task. Simulation results confirm the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Abstract To analyze the quantitative mapping relationship between the geometric errors of the five-axis CNC machine tool and the tooth surface deviation of spiral bevel gears, and identify the key geometric errors that affect the machining deviation of the spiral bevel gear tooth surface, a sensitivity analysis method for tooth surface machining deviation of spiral bevel gear based on screw theory and EFAST method is proposed. Firstly, the machining model of the spiral bevel gear tooth surface based on the five-axis CNC machine tool is established. Then, the geometric error transfer model of the machine tool is established based on the screw theory. Combined with the EFAST global sensitivity analysis method, the key geometric errors that affect tooth surface deviation are identified. Finally, the reliability and effectiveness tests are performed by comparing the results to the local sensitivity analysis method and simulating compensation for the key geometric errors. The result of compensation shows that the tooth surface deviation is reduced significantly according to global sensitivity analysis. The feasibility of applying sensitivity analysis to control the tooth surface deviation of spiral bevel gears has been demonstrated.

The theory of screws clarifies many analogies between apparently unrelated notions in mechanics, including the duality between forces and angular velocities. It is known that the real 6-dimensional space of screws can be endowed with an operator E , E 2 = 0 , that converts it into a rank 3 free module over the dual numbers. In this paper we prove the converse, namely, given a rank 3 free module over the dual numbers, endowed with orientation and a suitable scalar product (D -module geometry), we show that it is possible to define, in a canonical way, a Euclidean space so that each element of the module is represented by a screw vector field over it. The new approach has the effectiveness of motor calculus while being independent of any reduction point. It gives insights into the transference principle by showing that affine space geometry is basically vector space geometry over the dual numbers. The main results of screw theory are then recovered by using this point of view. [ABSTRACT FROM AUTHOR]

This paper reports an application of the Lie algebra s e (3) of the Euclidean group S E (3) , which is isomorphic to the theory of screws in the velocity and acceleration analyses of serial manipulators. The symbolic computation of the infinitesimal kinematics allows one to obtain algebraic expressions related to the kinematic characteristics of the end effector of the serial manipulator, while in the case of complex manipulators, numerical computations are preferred owing to the emergence of long terms. The algorithm presented enables the symbolic computation of the velocity and acceleration characteristics of the end effector in serial manipulators in order to allow the compact and efficient modeling of velocity and acceleration analyses of both parallel and serial robotic manipulators. Unlike other algebras, these procedures can be extended without significant effort to higher-order analyses such as the jerk and jounce. [ABSTRACT FROM AUTHOR]

Aiming at the problem of poor bearing capacity in the direction of decoupled DOF of weakly coupled three-translation parallel mechanism, a class of new configurations of large load-bearing capacity weakly coupled three-translation parallel mechanisms with closed-loop unit has been proposed in this paper. Based on the screw theory, configuration evolution method, and graphical approach method, the synthesis method of these kinds of mechanisms has been proposed, and the decoupled criterion of this mechanism and the addition conditions of the kinematic pair diagram are given. The synthesis process has been developed to synthesize the single degree of freedom translational decoupled branch chain and 2T coupled branch chain. To better apply the weakly coupled mechanism to large load occasions, a closed-loop unit construction method has been proposed. Based on the theory of singular value decomposition, a theoretical formula for increasing the load-bearing capacity of a mechanism by constructing a closed-loop unit with redundant drives has been derived for the first time. The closed-loop unit is added to the 2T coupled branch chain and the single DOF decoupled branch chain to construct the large load-bearing capacity single DOF decoupled three-translation parallel mechanism. Kinematic analysis and static analysis have been carried out on the synthesized mechanism. The Jacobian matrix of the synthesized mechanism is a block diagonal matrix, and the bearing capacity is significantly stronger than that of the decoupled mechanism, even higher than that of the coupled parallel mechanism. The synthesized weak coupling three translation parallel mechanism with large load bearing characteristics has a good application prospect in the field of high precision and large load bearing. [ABSTRACT FROM AUTHOR]

Most of the existing three-translation parallel mechanisms have more than one forward solution and are difficult to achieve precise and stable motion control. Therefore, a novel 3-RRPU parallel mechanism with three translational degrees of freedom was proposed, and the kinematics and dynamics and trajectory tracking control method of the parallel mechanism was researched. Firstly, by using the screw theory, the mechanism principle of implementing three translations was analyzed, and the drive input joints were chosen and demonstrated, and the characteristics of platform singularity, drive singularity, and branch-chain singularity of the parallel mechanism were analyzed. Secondly, the kinematics model of the parallel mechanism was built with the kinematics theory, and the forward and inverse position analytic solutions were derived. Thirdly, by using the Lagrange's dynamics theory, the rigid-body dynamics model of the parallel mechanism within the operating space was set up. Finally, a nonlinear feedback decoupled adaptive slide-mode trajectory tracking control method was proposed, and the stability of the trajectory control method was proved, based on the dynamics model of the parallel mechanism, the accuracy and drive moment simulations of the trajectory tracking control were implemented. The research results show that the mechanism has unique analytic forward position under general space configuration, and there are very few of the platform and drive singularity configurations of the mechanism and there is no branch-chain singularity configuration. The proposed trajectory tracking control method can enable the mechanism to achieve high-precision complex trajectory tracking of 0. 002 m under a load of 20 kg, a speed of 0. 18 m/ s, and an acceleration of 0. 12 m/ s², and especially, the trajectory tracking control method based on the Sigmoid function can effectively weaken chattering of the control moment, which provides new method for the implementation of three translational motions of high-speed, high-precision, and high-performance in the industrial field. [ABSTRACT FROM AUTHOR]

Traditional mobile robots have limited mobility in complex terrain environments. Generally, the closed-chain leg structure of a foot-type robot relies on the speed difference to turn, but it is difficult to complete the turning action in narrow spaces. Therefore, this study proposes a closed-chain foot-type robot that can move in multiple directions, inspired by the WATT-I leg structure. Firstly, the closed-chain single-leg structure is designed, and the leg structure is analyzed in terms of the degrees of freedom, kinematics, and singularity. A simulation is also carried out. Secondly, based on the present trajectory, a heuristic algorithm is used to solve the inverse trajectory problem, and the size of the mechanism is optimized. Finally, the steering mechanism of the leg with a zero turning radius is designed and analyzed, which achieves the steering function of the whole robot and satisfies the goal of enabling the foot robot to walk in all directions. This study provides theoretical guidance for the structural dimension optimization of the proposed foot mobile robot and its application in engineering fields such as rescue, exploration, and the military. [ABSTRACT FROM AUTHOR]

In this paper, a kind of hybrid kinematics chain with variable constraints is constructed by using a 6R spatial bifurcated chain and 4-DOF serial limbs, by using them, a 3-DOF Reconfigurable Parallel Mechanisms (RPM) was constructed, which has four motion modes: 3T, 2T1R, 2R1T, and 3R motion modes. Using screw theory, the change of wrench system in the hybrid kinematics chain caused by the reconfiguration of the 6R bifurcated chain is analyzed, which affects the wrench system of the moving platform (MP), and thus causes the reconfiguration of the parallel mechanism (PM). The triangular pyramid fixed to the MP was found as auxiliary geometry and used to intuitively describe the constraint relationship between joint axes in limbs. The latter was used to establish a unified forward kinematics model of the RPM in four motion modes. The general forward kinematics solution procedure for this type of RPM is given. The overall Jacobian matrix was obtained by screw theory for singularity analysis. The condition number of the Jacobian matrix measures the degree to which the mechanism is close to the singular configuration. Based on the Monte Carlo simulation, point cloud images representing the workspace of RPM were obtained. [ABSTRACT FROM AUTHOR]

Continuum robots, possessing great flexibility, can accomplish tasks in complex work scenes, regarded as an important direction in robotics. However, the current continuum robots are not satisfying enough in terms of fabrication and maintenance, and their workspace is limited by structure and other aspects. In this paper, to address the above problems, a modular deployable robot, which adopts an origami structure instead of a flexible hinge, is proposed. A fabrication method is innovated, the Spherical Linkage Parallel Mechanism (SLPM) unit is optimized, and the installation and fabrication process of the robot is simplified through modularization. The forward kinematics and inverse kinematics of the robot and its workspace are analyzed by using the screw theory. The prototype of the robot is constructed, and its folding performance, bending performance, and motion accuracy are tested, and the error analysis and compensation optimization are carried out. After the optimization, the position error of the robot is reduced by about 65%, and the standard deviation is greatly lowered, which effectively improves the motion accuracy and stability of the robot. [ABSTRACT FROM AUTHOR]

A decoupling method is proposed for the elastic stiffness modeling of hybrid robots based on the rigidity principle, screw theory, strain energy, and Castigliano's second theorem. It enables the decoupling of parallel and serial modules, as well as the individual contributions of each elastic component to the mechanism's stiffness performance. The method is implemented as follows: (1) formulate limb constraint wrenches and corresponding limb stiffness matrix based on the screw theory and strain energy, (2) formulate the overall stiffness matrix of parallel and serial modules corresponding to end of the hybrid robots based on the rigidity principle, principle of virtual work, the wrench transfer formula, and strain energy methods, and (3) obtain and decouple the overall stiffness matrix and deflection of the robot based on the Castigliano's second theorem. Finally, A planar hybrid structure and the 4SRRR + 6R hybrid robot are used as illustrative examples to implement the proposed method. The results indicate that selectively enhancing the stiffness performance of the mechanism is the most effective approach. [ABSTRACT FROM AUTHOR]

This article presents a parallel mechanism (PM) that is consists of a UPU and two RPU limbs (U, P, R denote universal joint, prismatic joint, and revolute joint, respectively). It can switch into two different configurations with three degrees of freedom (DOFs), in which one configuration outputs two rotations and one translation, and the other outputs two translations and one rotation. Four joints should be actuated to fully control the PM. Inverse position analysis is carried out. Taking the compliances of links into consideration, wrench analysis of the RU chain is conducted by using screw theory. Stiffness matrix and compliance matrix of the limb are derived through the strain energy method. The PM's overall stiffness matrix is then obtained according to the deformation compatibility equations. The theoretical results are compared with simulation results obtained in ANSYS, which shows a maximum deviation less than 0.6%. Static stiffness performance evaluation is carried out using the virtual work stiffness index. Performance distributions of the PM in two operation modes under external loads are obtained. The proposed stiffness modeling and performance evaluation could be helpful for optimal design and application investigation of the PM. [ABSTRACT FROM AUTHOR]

Geometric rotary axis errors are one of the main factors affecting the dispensing positioning accuracy of five-axis vision dispensing machines. Hence, the accurate detection and compensation of these error terms is an important and challenging problem. In this study, a decoupling identification method for both position-dependent geometric errors and position-independent geometric errors of a rotary dispensing table is proposed based on vision measurement technology. According to this strategy, the screw theory and exponential product formula are used to establish a kinematic model of the end-effector, followed by the definition of the mapping relationship between position-independent geometric errors and axis posture. Then, to separate the coupling error terms of the rotating axes, a step-by-step identification strategy is proposed based on the least squares method. Furthermore, a coordinate search-based error compensation algorithm is developed, which avoids the inverse singular value problem and is insensitive to the error model. Finally, the effectiveness of the proposed identification algorithm and compensation algorithm is experimentally validated. [ABSTRACT FROM AUTHOR]

Topological reconfiguration can improve the static stiffness and fault tolerance of parallel robots, but the problem of whether the robot can reach any specified pose without singular configuration has not been solved. Therefore, this paper takes the reconfigurable 3-RRR planar parallel robot as the research object, and proposes a path planning method that can realize “ point-to-point ” tracking. Firstly, the inverse kinematics model before reconfiguration is established, and six paths based on topological reconfiguration are found. Then, a “ four-step ” planning algorithm is constructed, which is suitable for “ point-to-point ” path tracking of reconfigurable parallel robots with any degree of freedom. It has intuitive geometric interpretation and can eliminate all singularities. The effectiveness of the planning algorithm is verified by an example. Further, based on the screw theory, the input and output transfer indexes under each input mode are calculated, and the optimal solution of the input mode is obtained by using the local transfer index. Finally, the “ point-topoint ” path planning algorithm is extended to continuous path planning. [ABSTRACT FROM AUTHOR]

To improve the carrying capacity of the robot, reduce the energy consumption of the driving motor and make the wheel-leg mode switching smooth and efficient, a reconfigurable decoupled parallel mobile robot configuration is proposed, and the configuration synthesis research and decoupling and singularity analysis are carried out. According to the expected degree of freedom of the robot's mechanical leg, four main motion limbs are synthesized. The 58 constraint limbs are synthesized based on the de-constraint method of the screw theory. Based on the virtual chain method of the screw theory, the 3R spherical parallel mechanism is synthesized as the bearing limb of the mechanical leg. Then two robot examples are given. Taking one of the robots as an example, the input-output equation is established, and the decoupling of the mechanical leg is analyzed. The singular configuration of the reconfigurable unit is verified by the reduction to absurdity, and the singular type is judged based on Grassmann line geometry. Finally, the influence of the singularity of the bearing limb on the motion output of the mechanical leg is analyzed. The mechanical leg of the robot adopts a parallel limb chain configuration, which has strong bearing capacity. The robot realizes wheel-leg switching based on constraint singularity, which makes the switching action more stable. The configurability of the mechanical leg reduces the energy consumption of the drive motor. Each drive of the mechanical leg is decoupled from the other, which reduces the control difficulty and makes the wheel-leg mode switching of the mechanical leg more efficient.

Abstract The current parallel ankle rehabilitation robot (ARR) suffers from the problem of difficult real-time alignment of the human-robot joint center of rotation, which may lead to secondary injuries to the patient. This study investigates type synthesis of a parallel self-alignment ankle rehabilitation robot (PSAARR) based on the kinematic characteristics of ankle joint rotation center drift from the perspective of introducing "suitable passive degrees of freedom (DOF)" with a suitable number and form. First, the self-alignment principle of parallel ARR was proposed by deriving conditions for transforming a human-robot closed chain (HRCC) formed by an ARR and human body into a kinematic suitable constrained system and introducing conditions of "decoupled" and "less limb". Second, the relationship between the self-alignment principle and actuation wrenches (twists) of PSAARR was analyzed with the velocity Jacobian matrix as a "bridge". Subsequently, the type synthesis conditions of PSAARR were proposed. Third, a PSAARR synthesis method was proposed based on the screw theory and type of PSAARR synthesis conducted. Finally, an HRCC kinematic model was established to verify the self-alignment capability of the PSAARR. In this study, 93 types of PSAARR limb structures were synthesized and the self-alignment capability of a human-robot joint axis was verified through kinematic analysis, which provides a theoretical basis for the design of such an ARR.

This paper introduces a four-legged decoupled Schönflies-motion generator parallel manipulator, free of passive limbs, provided with three linear actuators and one rotary actuator. The displacement analysis problem leads to closed-form solutions, thus avoiding the application of numerical methods for their solution, an unusual feature for most parallel manipulators. Subsequently, the theory of screws allows for solving the velocity, acceleration, and jerk analyses. Canceling the passive joint rates of the limbs is an indisputable advantage of the reciprocal-screw algebra. Moreover, upon the velocity analysis, the singularity analysis of the parallel manipulator is carried out by investigating the nature of the Jacobian matrices of the parallel manipulator. Then, we conclude that the robot at hand is free of type I and III singularities. Numerical examples enhance the correctness of the kinematic analysis method employed in the contribution. As far as the authors are aware, the topology of the parallel manipulator investigated here is original. [ABSTRACT FROM AUTHOR]

The D-H parameter method has found extensive application in the analysis of manipulator motion. However, it primarily describes motions along the x and z axes, neglecting the y-axis motion. To address this limitation, the present study employs the screw theory method to represent the manipulator's position and orientation as a screw, conducting an in-depth analysis of its kinematics and dynamics. In contrast to the traditional D-H approach for forward kinematics, screw theory offers a holistic depiction of the robot arm's motion, eliminating the necessity for an intermediate reference system with explicit geometric significance. To tackle the inverse kinematic problem of the elbow robotic arm, the Paden-Kahan subproblem is applied, resulting in the computation of an inverse kinematics solution. Leveraging screw theory and Lie group-Lie algebra, the Newton-Euler approach is employed to construct an efficient recursive dynamic model. Ultimately, the manipulator's inverse kinematic solution derived through the screw theory is subjected to simulation and verification, with its workspace calculation revealing that the screw theory method offers a more concise, accurate, and effective approach. [ABSTRACT FROM AUTHOR]

The current parallel ankle rehabilitation robot (ARR) suffers from the problem of difficult real-time alignment of the human-robot joint center of rotation, which may lead to secondary injuries to the patient. This study investigates type synthesis of a parallel self-alignment ankle rehabilitation robot (PSAARR) based on the kinematic characteristics of ankle joint rotation center drift from the perspective of introducing "suitable passive degrees of freedom (DOF)" with a suitable number and form. First, the self-alignment principle of parallel ARR was proposed by deriving conditions for transforming a human-robot closed chain (HRCC) formed by an ARR and human body into a kinematic suitable constrained system and introducing conditions of "decoupled" and "less limb". Second, the relationship between the self-alignment principle and actuation wrenches (twists) of PSAARR was analyzed with the velocity Jacobian matrix as a "bridge". Subsequently, the type synthesis conditions of PSAARR were proposed. Third, a PSAARR synthesis method was proposed based on the screw theory and type of PSAARR synthesis conducted. Finally, an HRCC kinematic model was established to verify the self-alignment capability of the PSAARR. In this study, 93 types of PSAARR limb structures were synthesized and the self-alignment capability of a human-robot joint axis was verified through kinematic analysis, which provides a theoretical basis for the design of such an ARR. [ABSTRACT FROM AUTHOR]

Abstract The pose accuracy of parallel manipulators (PMs) is a key index to measure their performance. Establishing the gravity-based kinetostatic model of a parallel robot provides an important basis for its error composition and accuracy improvement. In this paper, a kinetostatic modeling approach that takes real gravity distribution into consideration is proposed to analyze the influence of gravity on the infinitesimal twist and actuator forces of PMs. First, the duality of the twist screw and constraint wrenches are used to derive the gravity-attached constraint wrenches independent of the external load and the limb stiffness matrix corresponding to the kinematics-based constraint wrenches. Second, the gravity model of the mechanism is established based on the screw theory and the principle of virtual work. Finally, the analytical formulas of the infinitesimal twist and the actuator force of PMs are obtained, and the influences of the external load, platform gravity, and rod gravity on the stiffness of the mechanism are decoupled. The non-overconstrained 3RPS and overconstrained 2PRU-UPR PMs are taken as examples to verify the proposed method. This research proposes a methodology to analyze the infinitesimal deformation of the mechanism under the influence of gravity.

The seven-degree-of-freedom space manipulator, characterized by its redundant and aspheric wrist structure, is extensively used in space missions due to its exceptional dexterity and multi-joint capabilities. However, the non-spherical wrist structure presents challenges in solving inverse kinematics, as it cannot decouple joints using the Pieper criterion, unlike spherical wrist structures. To address this issue, this paper presents a closed-form analytical method for solving the inverse kinematics of seven-degree-of-freedom aspheric wrist space manipulators. The method begins by identifying the redundant joint through comparing the volumes of the workspace with different joints fixed. The redundant joint angle is then treated as a parametric joint angle, enabling the derivation of closed-form expressions for the non-parametric joint angles using screw theory. The optimal solution branch is identified through a comparative analysis of various self-motion manifold branches. Additionally, a hybrid approach, combining analytical and numerical methods, is proposed to optimize the parametric joint angle for a trajectory tracking task. Simulation results confirm the effectiveness of the proposed method.

Kinematics is a hot topic in robotic research, serving as a foundational step in the synthesis and analysis of robots. Forward kinematics and inverse kinematics are the prerequisite and foundation for motion control, trajectory planning, dynamic simulation, and precision guarantee of robotic manipulators. Both of them depend on the displacement models. Compared with the previous work, finite screw is proven to be the simplest and nonredundant mathematical tool for displacement description. Thus, it is used for displacement modelling of serial robots in this paper. Firstly, a finite-screw-based method for formulating displacement model is proposed, which is applicable for any serial robot. Secondly, the procedures for forward and inverse kinematics by solving the formulated displacement equation are discussed. Then, two typical serial robots with three translations and two rotations are taken as examples to illustrate the proposed method. Finally, through Matlab simulation, the obtained analytical expressions of kinematics are verified. The main contribution of the proposed method is that finite-screw-based displacement model is highly related with instantaneous-screw-based kinematic and dynamic models, providing an integrated modelling and analysis methodology for robotic mechanisms.

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Originating from the truss topology optimization of a cantilever beam model loaded at a single point at the end, this article introduces a novel cantilevered metamorphic mechanism that can transform between the space truss and the plane state. Firstly, by eliminating triangular sub-structures within the cantilevered truss, it accomplishes the truss-mechanism transformation and synthesizes the metamorphic mechanism with three configurations. Secondly, the product of exponentials is utilized to establish forward kinematics models, and we analyze the locations and velocities of three key nodes. Thirdly, for the dimensional synthesis of structure parameters and with the help of the space model, we draw performance atlases of the input transmission index. Finally, the case study is carried out based on a specific mechanism, and it finds that this metamorphic mechanism shows excellent kinematic performance. This work provides an important theoretical basis for engineering applications, and the metamorphic mechanism has great application potential in many fields such as aerospace, marine engineering, and robotics. Furthermore, this research will also inspire researchers to develop other metamorphic mechanisms. [ABSTRACT FROM AUTHOR]

A four-level rigid trunk mechanism based on 4-SPS/U, with SPS as the driving branch and U pair as the middle constrained driven branch, is innovatively proposed in this paper. Based on the innovative design of this trunk mechanism, it can improve the flexibility of the hexapod mobile robot's posture adjustment and changes in various motion modes such as walking, water propulsion, climbing and rolling. Firstly, the screw theory is adopted to calculate the degree of freedom of the trunk mechanism. Secondly, a combination of closed vector method and the characteristic structure configuration decoupling method has been applied to constructing the inverse kinematics solution, and deriving the velocity and acceleration models as well as analyzing the high posture flexibility in workspace of the trunk mechanism. Thirdly, theoretical simulation data diagram of the movement branch chain displacement, end height, speed and acceleration of the trunk mechanism are calculated through theoretical numerical examples, and the excellent motion characteristics of the 4-SPS/U-based four-level rigid trunk mechanism are analyzed. Finally, a quantitative comparison was made between the theoretical simulation data and the experimental data of the experimental prototype. The error rates of the variation curves of the displacement length, height, velocity and acceleration of the driving branch chain were 0.8%, 0.2%, 0.5% and 0.9%, which verified the correctness and reliability of the theoretical derivation. [ABSTRACT FROM AUTHOR]

The pose accuracy of parallel manipulators (PMs) is a key index to measure their performance. Establishing the gravity-based kinetostatic model of a parallel robot provides an important basis for its error composition and accuracy improvement. In this paper, a kinetostatic modeling approach that takes real gravity distribution into consideration is proposed to analyze the influence of gravity on the infinitesimal twist and actuator forces of PMs. First, the duality of the twist screw and constraint wrenches are used to derive the gravity-attached constraint wrenches independent of the external load and the limb stiffness matrix corresponding to the kinematics-based constraint wrenches. Second, the gravity model of the mechanism is established based on the screw theory and the principle of virtual work. Finally, the analytical formulas of the infinitesimal twist and the actuator force of PMs are obtained, and the influences of the external load, platform gravity, and rod gravity on the stiffness of the mechanism are decoupled. The non-overconstrained 3RPS and overconstrained 2PRU-UPR PMs are taken as examples to verify the proposed method. This research proposes a methodology to analyze the infinitesimal deformation of the mechanism under the influence of gravity. [ABSTRACT FROM AUTHOR]

A large-range-of-motion compliant transmission mechanism is introduced that uses the screw degrees-of-freedom (DOF) of a multi-DOF compliant module, sandwiched between two other single-DOF compliant modules, to convert a rotational input to a collinear translational output and vice versa. The geometric advantages (i.e., transmission ratios) of the mechanism when driven with a rotation to a translation or with a translation to a rotation can be tuned as desired. The freedom and constraint topologies (FACT) approach is used to design the mechanism, and stiffness matrices are used to explain why the transmission ratio of the mechanism is different depending on whether the mechanism is driven with its rotational or translational inputs. A version of the mechanism is fabricated and its transmission ratio is measured to be ~1.36 mm/deg when the mechanism is driven with a rotation, and is measured to be the inverse of ~1.89 mm/deg when the mechanism is driven with a translation. The transmission ratios both remain impressively constant over the mechanism's full range of motion and only vary slightly when they are actuated in different directions (i.e., counterclockwise or clockwise if the mechanism is driven with a rotation, or pushing or pulling if the mechanism is driven with a translation). [ABSTRACT FROM AUTHOR]

Abstract In order to solve the problem of weak stiffness of the existing fully decoupled parallel mechanism, a new synthesis method of fully decoupled three translational (3T) parallel mechanisms (PMs) with closed-loop units and high stiffness is proposed based on screw theory. Firstly, a new criterion for the full decoupled of PMs is presented that the reciprocal product of the transmission wrench screw matrix and the output twist screw matrix of PMs is a diagonal matrix, and all elements on the main diagonal are nonzero constants. The forms of the transmission wrench screws are determined by the criterion. Secondly, the forms of the actuated and unactuated screws can be obtained according to their relationships with the transmission wrench screws. The basic decoupled limbs are generated by combination of the above actuated and unactuated screws. Finally, a closed-loop units construction method is investigated to apply the decoupled mechanisms in a better way on the high stiffness occasion. The closed-loop units are constructed in the basic decoupled limbs to generate a high-stiffness fully decoupled 3T PM. Kinematic and stiffness analyses show that the Jacobian matrix is a diagonal matrix, and the stiffness is obviously higher than that of the coupling mechanisms, which verifies the correctness of the proposed synthesis method. The mechanism synthesized by this method has a good application prospect in vehicle durability test platform.

The cellular space robot (CSR) is a new type of self-reconfigurable robot. It can adapt the variety of on-orbit service tasks with large space spans through multi-level reconfiguration mechanisms. As the CSR has a large configuration space, kinematic solving becomes a key problem affecting on-orbit operation capability, and kinematic automatic solving research must be conducted. In order to solve this problem, firstly, the cellular space robot system capable of realizing multi-level self-reconfiguration is proposed for the demand of space on-orbit service, and the kinematic equations of modules are constructed by considering a single module function using screw theory. Secondly, the kinematics of the cellular space robot are encapsulated and divided into multiple levels, and the multilevel-assembly relationship-description method for robotic systems is proposed based on graph theory. On this basis, the pathway-solving algorithm is proposed to express the robot organization reachability information. Finally, the module–organ–robot multilevel kinematics solving algorithm is proposed in combination with screw theory. In order to verify the effectiveness of the algorithm in this paper, numerical simulation is used to compare with the proposed algorithm. The results show that compared with the traditional algorithm, the method in this paper only needs to update part of the assembly relations after organ migration, which simplifies the kinematic modeling operation and improves the efficiency of kinematic computation.

Continuum robots, possessing great flexibility, can accomplish tasks in complex work scenes, regarded as an important direction in robotics. However, the current continuum robots are not satisfying enough in terms of fabrication and maintenance, and their workspace is limited by structure and other aspects. In this paper, to address the above problems, a modular deployable robot, which adopts an origami structure instead of a flexible hinge, is proposed. A fabrication method is innovated, the Spherical Linkage Parallel Mechanism (SLPM) unit is optimized, and the installation and fabrication process of the robot is simplified through modularization. The forward kinematics and inverse kinematics of the robot and its workspace are analyzed by using the screw theory. The prototype of the robot is constructed, and its folding performance, bending performance, and motion accuracy are tested, and the error analysis and compensation optimization are carried out. After the optimization, the position error of the robot is reduced by about 65%, and the standard deviation is greatly lowered, which effectively improves the motion accuracy and stability of the robot.

This paper reports an application of the Lie algebra se(3) of the Euclidean group SE(3), which is isomorphic to the theory of screws in the velocity and acceleration analyses of serial manipulators. The symbolic computation of the infinitesimal kinematics allows one to obtain algebraic expressions related to the kinematic characteristics of the end effector of the serial manipulator, while in the case of complex manipulators, numerical computations are preferred owing to the emergence of long terms. The algorithm presented enables the symbolic computation of the velocity and acceleration characteristics of the end effector in serial manipulators in order to allow the compact and efficient modeling of velocity and acceleration analyses of both parallel and serial robotic manipulators. Unlike other algebras, these procedures can be extended without significant effort to higher-order analyses such as the jerk and jounce.

Traditional mobile robots have limited mobility in complex terrain environments. Generally, the closed-chain leg structure of a foot-type robot relies on the speed difference to turn, but it is difficult to complete the turning action in narrow spaces. Therefore, this study proposes a closed-chain foot-type robot that can move in multiple directions, inspired by the WATT-I leg structure. Firstly, the closed-chain single-leg structure is designed, and the leg structure is analyzed in terms of the degrees of freedom, kinematics, and singularity. A simulation is also carried out. Secondly, based on the present trajectory, a heuristic algorithm is used to solve the inverse trajectory problem, and the size of the mechanism is optimized. Finally, the steering mechanism of the leg with a zero turning radius is designed and analyzed, which achieves the steering function of the whole robot and satisfies the goal of enabling the foot robot to walk in all directions. This study provides theoretical guidance for the structural dimension optimization of the proposed foot mobile robot and its application in engineering fields such as rescue, exploration, and the military.