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Optical payloads are widely used in many fields, such as aerospace, drones, autonomous vehicles, or other highly precise instrumentation. Vibration is one of the causes that greatly affect the quality of data of highly precise optical payloads. Recently, many researcher focuses on isolating the vibration for the precise equipment, those study just only mention the overcoming of vibration in one or two directions, but in reality, an object will exist vibration in six directions in space. Therefore, it is necessary to find a new mechanism that can isolate vibration in six axes in space. The parallel mechanism is considered a viable system because of its strengths in accuracy, rigidity, and stability. In this research, the author proposes a novel 6-DOF passive vibration isolator based on the Steward platform with S-shaped legs. We have developed a 6-DOF passive vibration isolator using the S-shaped non-linear stiffness and damping characteristics. In this study, the model parameters of a vibration isolator device with legs using an S-shaped will be proposed. Based on geometrical parameters and vibration sources and some loads assuming the structure's durability problem will be calculated and evaluated the efficiency of the isolator at different frequencies. With the specially designed S-shaped it can be deformity like a spring, and with the change of structural and material parameters, we can adjust the system's stiffness and damping capacity. Due to the high static stiffness and low dynamic stiffness of each leg, and thus it is designable to isolate very well vibration isolation performance in all six directions. This research is organized as firstly the kinematics and 3D model are introduced. Secondly, the stiffness matrix of the novel 6-DOF passive vibration isolators is presented. Statics analysis of the 6-DOF passive vibration isolators revealed that the S-shaped structure provides sufficient load-carrying capacity and isolation due to its very good static nonlinear stiffness. The dynamic stiffness of the isolator in this study in each direction is very low but does not reduce the load-carrying capacity of the structure. By changing the structure and material parameters (which is very simple in a purely passive manner), we can completely adjust both the dynamic and static stiffness of the mechanism. The last series of numerical simulation results on displacement and a statics response in random excitation is carried out to show the effectiveness of the proposed 6-DOF passive vibration isolator, as well as the influence of structural parameters on vibration attenuation performance. The simulation results with the different exciting are shown to demonstrate the efficiency of the 6-DOF passive vibration isolators. Considering its simulation results A proposed new 6-DOF isolator will be applied in various engineering practices with multi-degree of freedom vibration isolation such as for precise optical payloa [ABSTRACT FROM AUTHOR]

Early detection and treatment of intraluminal diseases enable minimally invasive surgery and can lead to a high cure rate. Advanced devices with multiple degrees of freedom (DOFs) make narrow intraluminal procedures easier and safer. In a previous study, we developed a multi-DOF compliant endoluminal forceps with a tendon-sheath mechanism. The maximum bending stress of this design was reduced by changing the thickness of a compliant hinge in each segment, and the forceps achieved a wide range of motion. However, its deformed shapes with a non-constant curvature, due to a compliant inhomogeneous-thickness hinge structure, hinder fine manipulation in a narrow lumen. Here, we construct an accurate model of this compliant inhomogeneous-thickness hinge structure using pseudo-rigid-body model. In the proposed method, each compliant hinge is represented by a torsion spring and rotational joint, and the deformed shape is estimated from the bending angle caused by the tensile force. We derive the coefficient of dynamic friction by considering the friction between the wire and compliant joint based on a belt friction model. These novel calculations allow to consider individual differences in material properties and surface roughness. We experimentally confirm the feasibility of constructing a highly accurate model with a lower calculation cost than the finite element method. Our proposal seems suitable for developing dexterous forceps and other endoluminal devices, such as catheters, which mitigate operation errors and help approach lesions in narrow lumens. [ABSTRACT FROM AUTHOR]

The size of the oil pipes in the factory is relatively large, making them inconvenient to handle. There are few existing oil pipe handling devices, and a 2P2R four degree of freedom manipulator device has been innovatively designed to complete the oil pipe handling work. First, the three-dimensional model of the manipulator was established using SolidWorks software, and then the improved D-H method was used to carry out the kinematics modeling of the manipulator system, and the forward and Inverse kinematics equations were derived. Then, the MATLAB software was used to carry out the kinematics analysis of the manipulator, and the manipulator workspace was calculated. The movement trajectory, as well as the displacement, speed, and acceleration curves under the trajectory were obtained using the fifth order Polynomial interpolation method, Finally, the 3D model was imported into Adams software, and an Adams virtual prototype was established for dynamic analysis. The force and torque curves of each joint were obtained, laying the foundation for further design and research in the future. [ABSTRACT FROM AUTHOR]

This paper presents a comprehensive study of the forward and inverse kinematics of a six-degrees-of-freedom (DoF) spatial manipulator with a novel architecture. Developed by Systemantics India Pvt. Ltd., Bangalore, and designated as the H6A (i.e., Hybrid 6-Axis), this manipulator consists of two arm-like branches, which are attached to a rigid waist at the proximal end and are coupled together via a wrist assembly at the other. Kinematics of the manipulator is challenging due to the presence of two multi-DoF passive joints: a spherical joint in the right arm and a universal in the left. The forward kinematic problem has eight solutions, which are derived analytically in the closed form. The inverse kinematic problem leads to $160$ solutions and involves the derivation of a $40$ -degree polynomial equation, whose coefficients are obtained as closed-form symbolic expressions of the pose parameters of the end-effector, thus ensuring the generality of the results over all possible inputs. Furthermore, the analyses performed lead naturally to the conditions for various singularities involved, including certain non-trivial architecture singularities. The results are illustrated via numerical examples which are validated extensively. [ABSTRACT FROM AUTHOR]

The work defines in a new way the different types of solutions of the inverse kinematics (IK) problem for planar robots with a serial topology and presents an algorithm for solving it. The developed algorithm allows the finding of solutions for a wide range of robots by using a geometric approach, representing points in a polar coordinate system. Inverse kinematics, which is one of the most important, most studied and challenging problems in robotics, aims to calculate the values of the joint variables, given the desired position and orientation of the robot's end effector. Configuration space is defined by joint angles and is the basis of most motion planning algorithms. Areas in the working and configuration space are generated that are reachable with different types of solutions. Programs are created that use the proposed algorithm for robots with two and three rotational degrees of freedom, and graphically present the results in the workspace and configuration space. The possibility of transitioning from one type of solution to another by passing through a singular configuration is discussed. The results are important for planning motions in the workspace and configuration space, as well as for the design and kinematic analysis of robots. [ABSTRACT FROM AUTHOR]

• Instantaneous Kinematics (IK) of multi-DOF spatial mechanisms(SMs) is addressed • New geometric and analytic techniques for the analysis of this IK are presented • They relate multi-DOF SM's IK to the IK of the single-DOF SMs generated from it • They use Inst.-Screw-Axes (ISAs) and are implementable in a CAD system • The proposed methodology is relevant in mechanism design Multi-degree-of-freedom (multi-DOF) mechanisms generate single-DOF mechanisms by locking all their generalized coordinates but one. Here, the superposition principle is used to state a relationship between spatial multi-DOF mechanisms' instantaneous kinematics (IK) and the IK of the single-DOF mechanisms they generate. Firstly, the relationship between the instantaneous screw axes (ISAs) of a multi-DOF mechanism and the ISAs of the single-DOF mechanisms, it generates, is found; then, it is used for its singularity analysis. In particular, the IK model of a generic multi-DOF spatial mechanism is written through the ISA locations and, successively, it is studied to identify all the singular configurations of the multi-DOF mechanism through the analysis of the single-DOF mechanisms it generates. The results are a technique for the determination of ISAs' locations in multi-DOF spatial mechanisms and a singularity-analysis technique, for the same mechanism types, based on the singularity analysis of single-DOF spatial mechanisms. Eventually, the proposed techniques are applied to a case study. As far as this author is aware, both these results are presented for the first time in the literature. [ABSTRACT FROM AUTHOR]

Based on the traditional three degree of freedom (DOF) planar parallel mechanism, a novel reconfigurable 3-DOF planar parallel mechanism is proposed. Firstly, based on the theory and method of topology design of the parallel mechanism position and orientation characteristic (POC). The switch between the 3-revolute-joint, prismatic-joint, revolute-joint (3-RPR) and 3-revolute-joint, revolute-joint, revolute-joint (3-RRR) planar parallel mechanisms is realized through a reconfigurable branch chain. Then, taking 3-RRR configuration as an example, the important topological indexes of the mechanism, such as POC, DOF and coupling degree, are analyzed. Based on the structural characteristics and geometric constraints of the mechanism, the inverse kinematics model is derived by using the closed vector method. Finally, the position workspace of the mechanism is analyzed based on the geometric constraint method of the branched chain and the inverse solution model respectively. This work provides not only a new idea for the analysis of mechanism workspace, but also a new choice for the design of mechanism. [ABSTRACT FROM AUTHOR]

In this paper, a novel four degrees-of-freedom (4DOF) articulated parallel forceps mechanism with a large orientation workspace (± 90 deg in pitch and yaw, 360 deg in roll rotations) is presented for robotic minimally invasive surgery. The proposed 3RSR-1UUP parallel mechanism utilizes a UUP center leg that can convert thrust motion of the 3RSR mechanism into gripping motion. This design eliminates the need for an additional gripper actuator, but also introduces the problem of unintentional gripper opening/closing due to parasitic motion of the 3RSR mechanism. Here, position kinematics of the proposed mechanism, including the workspace, is analyzed in detail, and a solution to the parasitic motion problem is provided. Human-in-the-loop simulations with a haptic interface are also performed to confirm the feasibility of the proposed design. [ABSTRACT FROM AUTHOR]

In view of the fact that the transmission mode of the multi-DOF motor hinders its further development, the gas bearing is applied to the multi-DOF motor to form a new structure of the multi-DOF motor with air-floation (AMM). AMM not only improves the motor's motion characteristics and transmission performance, but also basically does not cause environmental pollution. AMM uses porous static pressure gas bearing as the support structure, and completes the multi-DOF movement by controlling the energizing strategy of the coils. This paper introduces the structure of AMM, analyzes the basic working principle of AMM, and solves the air gap magnetic field; the kinematics model of the motor is established, the motion of the motor is controlled with the help of virtual simulation software, and the motion trajectory of the motor is obtained through the marked points of the output shaft. Finally, the AMM was verified by experiments, the error of experiment and simulation was controlled at 5%, and the kinematics characteristics of the motor met the design requirements. The research results provide a new idea for the development of multi-DOF motor. [ABSTRACT FROM AUTHOR]

A human hand is a complex biomechanical system, in which bones, ligaments, and musculotendon units dynamically interact to produce seemingly simple motions. A new physiological hand simulator has been developed, in which electromechanical actuators apply load to the tendons of extrinsic hand and wrist muscles to recreate movements in cadaveric specimens in a biofidelic way. This novel simulator simultaneously and independently controls the movements of the wrist (flexion/extension and radio-ulnar deviation) and flexion/extension of the fingers and thumb. Control of these four degrees of freedom (DOF) is made possible by actuating eleven extrinsic muscles of the hand. The coupled dynamics of the wrist, fingers, and thumb, and the over-actuated nature of the human musculoskeletal system make feedback control of hand movements challenging. Two control algorithms were developed and tested. The optimal controller relies on an optimization algorithm to calculate the required tendon tensions using the collective error in all DOFs, and the action-based controller loads the tendons solely based on their actions on the controlled DOFs (e.g., activating all flexors if a flexing moment is required). Both controllers resulted in hand movements with small errors from the reference trajectories ($< 3.4^\circ$); however, the optimal controller achieved this with 16% lower total force. Owing to its simpler structure, the action-based controller was extended to enable feedback control of grip force. This simulator has been shown to be a highly repeatable tool ($< 0.25$  N and $< 0.2^\circ$ variations in force and kinematics, respectively) for in vitro analyses of human hand biomechanics. [ABSTRACT FROM AUTHOR]

Machine tools with multiple degrees of freedom and parallel kinematics offer tremendous opportunities for new kind of processes but at the same time also a lot of control challenges. They are subject to uncertainties in the form of kinematic errors, elasticities and thermal deflections. Their kinematic non-linearity requires the application of model-based control concepts whose full effectiveness can only be unlocked through controls in the task space. In particular, kinematic singularities occur in forming machines such as presses, which make closed-loop control at corresponding operating points considerably more difficult. In this paper, we use the example of a servo-driven press with three ram degrees of freedom to show how parallel kinematic machine tools can be controlled via inverse differential kinematics models in task space and to what extent the controls can benefit from scheduled gain factors. The results are validated both simulatively and experimentally. In the experimental tests, three-dimensional tool paths are traced that can be used to carry out orbital forging processes. Furthermore, the example of a punch hole rolling process demonstrates that the ram pose is controlled more accurately, which also has positive effects on the resulting workpiece geometry. The performance of the developed gain scheduling task space control is compared with that of a robust and non-robust control with static gains. • Parallel kinematic machine tools are hard to control in task space • Task space control requires integration of sensors in the vicinity of the TCP • Controlling the bearing position of the TCP platform allows gain scheduled control • Gain scheduled control with better performance than conventional control • Superiority of the control also visible in produced workpiece geometries [ABSTRACT FROM AUTHOR]

This work solves the regulation and tracking trajectories tasks for four degrees of freedom anthropomorphic robot manipulators. Two controllers are considered: a Super-Twisting controller (ST) and a Proportional Derivative with dynamics compensation (PD+) control. This comparison is carried out through numeric simulation of the dynamic model in the presence of disturbances using Matlab-Simulink software. Also, the tuning procedure of each controller is shown, as well as the stability criteria used for each case. The tunning of the ST controller is done considering the effects produced by an unknown Lipschitz disturbance; this guarantees robustness against this kind of disturbance. The results of the ST controller show the rejection of the disturbance, allowing the correct trajectory tracking. An algorithm based on the inverse kinematics solution is used to generate trajectories and their interpretation in generalized coordinates corresponding to the manipulator's joint positions obtained through the geometric approach. In addition, we show the workspace, the manipulator parameterization, and the manipulator dynamic model through the Euler- Lagrange motion equations. [ABSTRACT FROM AUTHOR]

Advances in materials, design, and control, as well as increasing concerns about the sustainability of the built environment, have provided a background for the development of deployable tensegrity and scissor-like systems, which are often limited between a closed and an open state. In cases where more versatile reconfigurations are aimed at, the systems rely on embedded computation and mechanical actuators. Such mechanisms often lead to energy-inefficient operation and complex kinematic behavior. Toward providing multiple possible target configurations of the structure, as well as flexibility and controllability, the effective crank–slider and effective 4-bar methods have been proposed and applied to planar multibar linkage systems. The underlying kinematics principle refers to the reduction of a multi-DOF system to an externally actuated 1-DOF system in each reconfiguration step of the control sequence while adjusting the system joints from an initial to a target position. The present paper reviews related aspects with regard to the two basic reconfiguration approaches and exemplifies their combined implementation through a case study concerning a closed-chain linkage system with eight bars. [ABSTRACT FROM AUTHOR]

Inverse kinematic solution is a critical procedure for the control of manipulators; however, only a small number of manipulators that meet certain conditions have closed-form solutions. In this paper, the conventional solution was replaced by the optimization process of a proposed fitness function. The fitness function aims to obtain a set of accurate joint angles for the desired position and orientation of the end effector. The function is based on forward kinematics; hence, this approach can avoid singularities and be suitable for solving many manipulators. For solving this optimization problem, particle swarm optimization algorithm was chosen as the basis due to its easy principle and excellent performance. To enhance the performance of the algorithm in searching global optimum, an adaptive inertia weight strategy applied to adjust the velocity of particles was proposed. Besides, for particles, to avoid trapping in local optimum at the boundary, a special boundary treatment was presented. In this study, two serial robotic manipulators were used to test the performance of adaptive particle swarm optimization (APSO). Meanwhile, several powerful PSO variants improved from disparate methods were selected to compare with APSO. The experimental results demonstrate that the proposed fitness function with APSO can solve the inverse kinematic problem of multi-DOF manipulators efficiently and accurately. [ABSTRACT FROM AUTHOR]

• The mobility of mechanisms comprising spatial scissor units are analyzed. • The translational assembly has 4 DOFs, while the 4th DOF is infinitesimal. • The mirrored assembly has a single DOF and thus can be deployed in one mode. Mechanisms consisting of spatial scissor units have different kinematic behaviors than those of planar scissors. However, their kinematics, especially the mobility analysis, has not received enough attention. Two types of deployable assemblies are analyzed in this paper, namely the translational and mirrored assemblies. Both the assemblies are made of tripod scissor units, and their instantaneous mobility are examined using screw theory. The study starts on the configuration where all the members have the identical deployment angle. Firstly, the geometric property of each assembly was studied. Then, screw-loop equations were developed based on graph theory and closure equations. Finally, the mobility of each assembly was computed using linear algebra. Following the analysis, physical prototypes were constructed to validate the results, and several different motion modes were obtained for the translational assembly. The analysis reveals different kinematic behaviors of the two assemblies. In the given configuration, the translational assemblies have four instantaneous degrees of freedom, while the mirrored assemblies have only a single instantaneous degree of freedom. [ABSTRACT FROM AUTHOR]

This paper presents a new trajectory planning method based on the improved quintic B-splines curves for a three degrees-of-freedom (3-DOF) cable-driven parallel robot (CDPR). First, the conditions of positive cables’ tension are expressed in terms of the position and acceleration constraints of the end-effector. Then, an improved B-spline curve is introduced, which is employed for generating a pick-and-place path by interpolating a set of given via-points. Meanwhile, by expressing the position and acceleration of the end-effector in terms of the first and second derivatives of the improved B-spline, the cable tension constraints are described in the form of B-spline parameters. According to the properties of the defined pick-and-place path, the proposed motion profile is dominated by two factors: the time taken for the end-effector to pass through all the via-points and the ratio between the nodes of B-spline. The two factors are determined through multi-objective optimization based on the efficiency coefficient method. Finally, experimental results on a 3-DOF CDPR show that the improved B-spline exhibits overall superior behavior in terms of velocity, acceleration, and cables force compared with the traditional B-spline. The validity of the proposed trajectory planning method is proved through the experiments. [ABSTRACT FROM AUTHOR]

Parallel continuum mechanisms are a type of compliant mechanisms comprising a rigid end-effector connected to a fixed frame by flexible and slender elements in a closed-kinematic morphology, being their flexibility the source of mobility. Solving the position problem involves the static equilibrium of the whole device considering the nonlinear large deformations of slender elements. Numerical iterative solutions are already available to solve real-time simulations. However, an assembled solution, which meets both geometric conditions and static equilibrium, is needed to start the process. A comprehensive Kinematic Analysis in the classical sense is not fully established yet. The aim of the paper is to propose a procedure that solves the full inverse and forward kinematic problems for planar three degrees of freedom systems, hence obtaining the multiple solutions arising from the closed-loop structure and the multiplicity of the deformation mode of slender links. From those solutions, finding of the different aspects that comprise the workspace is possible, as well as determining singularities and instability loci. • To find multiple solutions of position problem of 3 DoF planar parallel continuum mechanisms. • Kirchhoff planar deformation rod model integrated using elliptic integrals. • Multiple solutions in association with variability of buckling modes. • Obtaining aspects of the workspace, singularities and instability loci. [ABSTRACT FROM AUTHOR]

The kinematics and redundant space analysis of redundant robots constitutes important research content. Currently, methods such as geometric method and iterative optimization method are relatively complicated and inconvenient for programming and practical control applications. Moreover, little research has been conducted on redundant space analysis. This paper takes the 4-DOF PowerCube redundant robot as the research object. The forward and inverse kinematics equation of the robot are established based on the D-H matrix method, projection and cosine theorem method, and vector coordinate method. Then, the redundant space of the robot is obtained and the redundant space range of the robot is analyzed. Finally, the simulation of kinematic and redundant space research is conducted. It is shown that the change of each joint angle of the robot is smooth without mutation, so it can ensure the stable motion of the robot. Additionally, the different position and redundant variable have a big influence on robotic configuration. The calculation amount is relatively small and convenient for programming application, and the path calculation data of the joints are obtained, which are conducive to the motion control of modular robots. The method used in this paper can be extended to the multi-DOF redundant robot. Finally, the motion optimization, control, and obstacle-avoidance of redundant robots are briefly studied. The results of this paper provide an important basis for these aspects of research. [ABSTRACT FROM AUTHOR]

A four degrees-of-freedom (DOF) Parallel Manipulator (PM) with a 4 P Pa-2PaR configuration has been proposed to generate 3-DOF Translational and 1-DOF Rotational (3T1R) motions in our early work. It has the advantages of symmetric geometry, simple kinematics and infinite extension of translational workspace along its linear guide direction. However, its V-type assembly mode results in a long distance between its moving platform and the base, which makes its stiffness and accuracy lower. Besides, its the other two translational workspaces are limited due to its kinematic singularities. To overcome such limitations, the PM is modified by utilizing its M-type assembly mode and placing an offset angle to the last parallelogram mechanism. To simplify the displacement analysis, a geometrical projection method is employed, while a closed-loop vector approach is used for its instantaneous kinematic analysis. Both singularity and workspace issues are investigated. An optimization algorithm based on Genetic Algorithm is proposed to maximize the reachable workspace. The optimization result indicates that the workspace is significantly increased. A prototype of the M-type PM is fabricated to validate the effectiveness of the modified design. • A modified 4-DOF 3T1R parallel manipulator with M-type assembly mode is proposed. • An offset angle is placed to the last parallelogram to enlarge the workspace. • A geometrical projection method is employed to simplify the kinematic analysis. • The workspace in x – o – z plane is significantly increased through design optimization. [ABSTRACT FROM AUTHOR]

The ability to measure six degrees of freedom (6 DOF) head kinematics in motor vehicle crash conditions is important for assessing head-neck loads as well as brain injuries. A method for obtaining accurate 6 DOF head kinematics in short duration impact conditions is proposed and validated in this study. The proposed methodology utilizes six accelerometers and three angular rate sensors (6aω configuration) such that cm algebraic equation is used to determine angular acceleration with respect to the body-fixed coordinate system, and angular velocity is measured directly rather than numerically integrating the angular acceleration. Head impact tests to validate the method were conducted using the internal nine accelerometer head of the Hybrid III dummy and the proposed 6avj scheme in both low (2.3 m/s) and high (4.0 m/s) speed impact conditions. The 6aw method was compared with a nine accelerometer array sensor package (NAP) as well as a configuration of three accelerometers and three angular rate sensors (3aω), both of which have been commonly used to measure 6 DOF kinematics of the head for assessment of brain and neck injuries. The ability of each of the three methods (6aω, 3aω, and NAP) to accurately measure 6 DOF head kinematics was quantified by calculating the normalized root mean squared deviation (NRMSD), which provides an average percent error over time. Results from the head impact tests indicate that the proposed 6aaj scheme is capable of producing angular accelerations and linear accelerations transformed to a remote location that are comparable to that determined from the NAP scheme in both low and high speed impact conditions. The 3aω scheme was found to be unable to provide accurate angular accelerations or linear accelerations transformed to a remote location in the high speed head impact condition due to the required numerical differentiation. Both the 6aω and 3aω schemes were capable of measuring accurate angular displacement while the NAP instrumentation was unable to produce accurate angular displacement due to double numerical integration. The proposed 6ao scheme appears to be capable of measuring accurate 6 DOF kinematics of the head in any severity of impact conditions. [ABSTRACT FROM AUTHOR]

Abstract: In Part II of this paper we demonstrate how to use freedom and constraint topology (FACT) to synthesize concepts for the multi-degree of freedom, parallel precision flexure systems that fall within the scope of Part I. Several examples are provided to demonstrate how the Principle of Complementary Topologies and geometric entities from Part I are (i) relevant to flexure system characteristics, (ii) used to visualize the possible layout of flexure constraints to achieve a desired motion and (iii) used to select redundant constraints. A synthesis process is presented, and then used to visualize and construct a flexure system concept with the requisite kinematic characteristics and redundant constraints that provide increased stiffness, load capacity, and symmetry. The output of the process is a flexure concept that would then be modeled and refined by existing modeling and analysis methods. [Copyright &y& Elsevier]

This paper investigates a novel position-sensor-based force reflection framework for multi-degree-of-freedom (DOF) bilateral teleoperation systems in unstructured environments. The conventional position-sensor-based force reflection method, which is known as position error feedback, may generate grossly inaccurate force reflection directions during collisions involving the slave manipulator links. The proposed restriction space projection framework calculates the instantaneous restriction space to provide the accurate force reflection, regardless of kinematic dissimilarity (KDS) conditions of bilateral teleoperation systems. Simulation results confirmed the validity of the proposed framework in a KDS bilateral teleoperation system under various constraint conditions. [ABSTRACT FROM AUTHOR]