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• 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]

• 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]

• Cable-driven gravity compensation mechanism for spatial multi-DoF robotic systems. • Application example of an exoskeleton for proposing and analyzing the mechanism. • Mechanical model design for evaluating the mechanism's technical feasibility. • Effectiveness validation by calculating and analyzing the cable tension. The gravity compensation mechanisms (GCMs) are widely used in robotic manipulators and exoskeletons. This paper presents a cable-driven GCM applied in a spatial multi-degree-of-freedom (DoF) robotic system. By combining the cable transmission with the spring-based GCM, the whole compensation system is placed outside the main body of the robotic system, including the movable links and revolute joints. Therefore, the complexity and inertia of the robotic system's main body are reduced, and the motion range will not be limited by the mechanism for compensation, such as parallelogram linkages. Here presents the application example of a cable-driven four-DoF exoskeleton to demonstrate the development of the proposed GCM. The GCM is analyzed based on the space mapping method, and the mechanical models are designed based on theoretical analysis to evaluate the technical feasibility. The effectiveness of the proposed GCM is validated by calculating and analyzing the cable tension required by the exoskeleton and generated by the GCM in several specific movements. Finally, some limitations and potential applications of this cable-driven GCM are discussed. [ABSTRACT FROM AUTHOR]

• A novel Schatz-based omnidirectional mobile mechanism adopts Oloid-like paddlewheels is proposed. • Four basic locomotion gaits are designed according to the kinematics of the mechanism. • Based on the basic gaits, the moving performance of the mechanism on typical terrains is discussed. • A prototype is manufactured to test the functions of the mechanism. In this paper, a novel Schatz-based omnidirectional mobile mechanism adopting Oloid-like paddlewheels with a total of four degrees of freedom (DOFs) is proposed. It is composed of four diagonally arranged Schatz linkages, and taking the advantage of Oloid surface, the link of each Schatz linkage is designed as the Oloid-like shape to adapt to variable terrain. Then according to the kinematics of the mechanism, the omnidirectional locomotion gaits, including the straight-going gait, the lateral moving gait, the oblique moving gait and the turning gait, are designed and analyzed. Based on these basic gaits, the moving performance of the mechanism in slope climbing, stair climbing and water stroking is analyzed. Finally, a prototype is manufactured and moving experiments are carried out to verify the locomotion performance of the mechanism. [ABSTRACT FROM AUTHOR]

This article presents the compliant manipulator design method (COMAD) for the synthesis of serial and parallel multi-DoF compliant mechanisms. Currently, the freedom and constraint topology (FACT)-method results in flexure systems being a serial kinematic solution for multi-DoF motions. In the COMAD method parallel solutions are included too through 3 steps: (1) obtaining the serial and parallel kinematic solutions for an intended set of end-effector DoFs with the type synthesis of legs-method ; (2) transforming each legtype into a flexure leg by using the FACT method; (3) combining legs in parallel to obtain complete compliant mechanism designs. It was applied for a compliant Schönflies motion generator – having three translations and one rotation – resulting in 5 different 4-DoF flexure legs. 4 designs were new compared to the result obtained using the FACT method. Then, a set of legs was combined in parallel resulting in a compliant Schönflies mechanism, which was manufactured. Its mobility was experimentally evaluated by modal analysis. The intended motions separately became visible during its first four eigenmodes. They are the mechanism's DoFs as their stiffness is relatively low. • It is a synthesis method for multi-DoF serial and parallel compliant mechanisms. • In 3 steps, the "type synthesis of legs" method and the "FACT"-method are combined. • For a Schönflies 4 DoF motion generator 5 flexure leg designs were found; 4 new ones. • Experimental validation of the mechanism's 4 DoFs by modal analysis. [ABSTRACT FROM AUTHOR]

Highlights • A time-varying and piecewise dynamic model is developed to investigate the vibration characteristics of a multi-degree-of-freedom feed system. • The inertial forces of linear guide, ball screw and ball bearing are analyzed by considering contact characteristics and the model is verified by experimental results. • The coupling effects among vibrations, excitation amplitude and screw-nut position on the dynamic characteristics and stability are investigated. • Some practical guidelines are proposed to suppress the vibration and achieve stability. Abstract In this study, a multi-degree-of-freedom model is developed to investigate the vibration characteristics of a feed system with nonlinear kinematic joints. Linear guide, ball screw, and ball bearing are the main kinematic joints that connect and support the worktable of a feed system. Considering the contact behaviors of rolling balls, contact force is a piecewise smooth function of displacements of the multi-degree-of-freedom system. In terms of modeling, geometry and material parameters are determined according to the experimental feed system and the model is verified by a dynamic experiment. The motion equations of the system are derived to evaluate the effects of force excitation and screw-nut position on the vibration amplitude and stable state of the vibratory system. With the variation of screw-nut position, there exist jumping phenomena for displacement and deformation amplitude near the resonance frequency region. The hardening and softening type nonlinearity, super harmonic resonance, jumping phenomenon and chaotic motion are strongly attributed to the coupling vibrations. The application of the multi-degree-of-freedom model can supply information to suppress vibration and improve processing precision. [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]

This paper addresses the stability of macro–mini robotic systems in a context of physical human–robot interaction (pHRI). A simple model including a one-degree-of-freedom (one-dof) macro robot and a one-dof mini robot is investigated using a state-space representation in order to assess the controllability and stability of the system. In this work, the stability of the system is analysed in more detail regarding two perspectives of the interaction process, namely the human force input and the human position input. Moreover, physical limits and the frequency response of the macro–mini system are also examined. Therefrom, this study derives a general formula for the constraints of the virtual mass and the virtual damping. Possible choices of these parameters in certain ranges are graphically and visually demonstrated. Simulations are carried out in order to demonstrate the stability and the behaviour of the system with different input signals. The conclusions of the analysis can be used in the design of multi-dof macro–mini systems. An example of a 12-dof macro–mini system is briefly described to illustrate potential applications. • The dynamic modelling of macro–mini robotic systems. • A stability analysis of macro–mini robotic systems. • Proposed controller design for macro–mini robotic systems. • Simulation results that demonstrate the stability. • Design guidelines for the selection of the rendered mass and damping. [ABSTRACT FROM AUTHOR]

• A novel dynamics-analysis method for multi-DOF planar mechanisms is presented. • The presented method holds for all the planar mechanisms. • The proposed method fully discloses instant centers' role in dynamics analyses. • A geometric interpretation of the deduced dynamic model is provided. • The presented results are of interest in planar mechanisms' analysis and design. Most approaches of analytical mechanics (e.g., D'Alembert principle) build dynamic models of mechanisms that are difficult to relate with clear geometric interpretations. This feature is a drawback that confines their use to the implementation of algorithms in multi-body-dynamics software, whose results must be interpreted by using the designer intuition when the mechanism must be modified to match particular design requirements. Here, starting from D'Alembert principle, the dynamic model of any multi-degrees-of-freedom (multi-DOF) planar mechanism (PM) is obtained by suitably combining the dynamic models of all the single-DOF PMs generated by locking all the actuated joints, but one. The dynamic models of the so-generated single-DOF PMs are written by using an approach, presented in a previous paper, which admits a geometric interpretation through diagrams, named "active-load diagrams", and fully discloses the role of instant centers (ICs) in the dynamic behavior of single-DOF PMs. Accordingly, the resulting dynamic model of the generating multi-DOF PM admits a geometric interpretation that reveals the role of ICs in multi-DOF PMs' dynamic behavior. Such geometric interpretation is so effective that, formally, the model could be written starting from it without any analytic consideration the same way as the equilibrium equations can be written from free-body diagrams in the Newton-Euler formulation. The presented model is general and, as far as this author is aware, is novel. The proposed model and the associated algorithms for solving dynamic problems are also illustrated through a case study. The obtained results are of interest in mechanism analysis and design. [ABSTRACT FROM AUTHOR]

• Rigid-body displacements of time-varying models can be eliminated in modal coordinates. • Some modal responses of split-path transmissions can be suppressed by mesh phasing. • Vibrations in some directions can also be suppressed for different parameters. • The suppression phenomenon is interpreted as decoupling from excitations. This paper studies the effectiveness of adopting mesh phasing for suppressing several particular modal responses in a typical split-path transmission. The dynamic model admits three planar degrees of freedom for each gear and considers time-varying mesh stiffnesses, which captures the effect of mesh phasing. The vibration modes of the system are analyzed for the time-invariant case with average mesh stiffnesses, and the characteristics of each mode shape are summarized. Then, according to the characteristic of rigid-body modes, a new method for eliminating the rigid-body displacement of a time-variant system is proposed. This method has a clear physical interpretation and is convenient to use. The modal equations are solved numerically after removal of the equation of the rigid-body mode. It is found that appropriate mesh phasing can effectively suppress several different modal responses, and a physical interpretation of this phenomenon is provided by using the modal equations and the modal analysis results. [ABSTRACT FROM AUTHOR]

• Propose a type synthesis method to design 2R1T RCM PMs with a passive limb. • Propose several novel 2R RCM composite joints and 2R1T RCM passive limbs. • Obtain numerous 2R1T RCM PMs with a passive limb. • Propose evaluation criteria that enable the selection of the optimal designs. In view of the demands for medical imaging compatibility and efficient space occupation around the surgical site, this paper proposes remote center of motion (RCM) parallel mechanisms (PMs) with a passive limb to enable more flexible arrangement of the limbs and actuators in a RCM surgical manipulator. A type synthesis method is proposed to design the 2R1T RCM PMs with a passive limb based on the Lie group. The motion requirements for the RCM mechanism are first expressed in the form of Lie group. The motion arrangement and kinematic structure development are then implemented to obtain the active and passive limbs. By means of this approach, numerous 2R1T RCM PMs with a passive limb are synthesized. The actuated joints are then selected, and a few qualitative evaluation indices are proposed. Finally, the motion configurations of two generated mechanisms are validated through simulation. The proposed method is universally effective for the type synthesis of multi-degree of freedom RCM PMs with a passive limb. [ABSTRACT FROM AUTHOR]

This paper addresses the robust control problem of mechanical systems with hybrid dynamics in port-Hamiltonian form. It is assumed that only the position states are measurable, and time-delay and saturation constraint affect the control signal. An extended state observer is designed after a coordinate transformation. The effect of the time delay in the control signal is neutralized by applying Padé approximant and augmenting the system states. An assistant system with faster convergence is developed to handle actuators saturation. Fractional-order sliding mode controller acts as a centralized controller and compensates for the undesired effects of unknown external disturbance and parameter uncertainties using the observer estimation results. Stability analysis shows that the closed-loop system states, such as the observer tracking error, and the position/velocity tracking errors, are finite-time stable. Simulation studies on a two ball-playing juggler robot with three degrees of freedom validate the theoretical results' effectiveness. • System states and lumped disturbance are estimated by extended state observer. • Two auxiliary systems are designed to handle input delay and actuator saturation. • Based on fractional calculus, a robust centralized controller is designed. • The robustness and finite-time stability of the closed-loop system are fulfilled. [ABSTRACT FROM AUTHOR]

• A synthesis method for eliminating isomorphism identification based on graph similarity is proposed. • Similar edges are further divided into two types, i.e., CESE and IESE. • The internal relations between similar edges and isomorphism are revealed. • Kinematic chains with up to seven loops and three DOFs are exposed. • All the synthesis process can be realized automatically by the computer. A novel method for eliminating isomorphism identification is proposed to improve synthesis efficiency and synthesize planar nonfractionated kinematic chain (KCs) automatically. This method is based on the vertex insertion of contracted graphs. First, similar edges of contracted graphs are divided into groups, in which the similar edges are found and their characteristic matrices are calculated. The edge types are divided based on whether or not isomerism occurs after vertices are inserted. Then, the vertices are inserted into contracted graphs according to the edge condition. In this process, all isomerism caused by the location and number of inserted vertices is reserved, and the property change of similar edges is checked. Lastly, the rigid subchains of remaining isomerism are distinguished. Contracted graphs with four independent loops and some of their inserted vertices are presented in appendix. A complete set of nonfractionated KCs with up to seven independent loops and three degrees of freedom is also provided. The veracity and efficiency of the method are confirmed by conducting a comparative analysis between this synthesis and other literature results. [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]

Abstract: The dynamic behaviour of cracked rotors is one of the most discussed topics in the rotordynamic literature due to the wide range of problems that may arise from this fault. Among them, it is a common notion that cracks in horizontal rotating shafts may cause instability of the system because of the periodic opening and closing of the crack, i.e., the breathing mechanism, determines the stiffness variation and the parametric excitation of the rotor system. Simplified models have been used to study this phenomenon using Jeffcott rotors. For the first time in this paper, a model of a real hyperstatic rotor with several degrees of freedom is used, which also considers the bearings and the foundation of the system, and the stability is discussed by means of the Floquet theory. The sensitivity of the obtained results to the system anisotropy and the crack position is also investigated. The results presented are quite different from those obtained by means of the simple Jeffcott rotor but are consistent with real and documented field experiences. [Copyright &y& Elsevier]

l A systematic method for synthesizing single-loop 3 T 1 R -PMs is proposed. l Two structures are introduced to construct 3 T 1 R -PMs with a full circle rotation function. l Two types of single-loop 3 T 1 R -PMs with a multi-DOF drive system are synthesized. l The simulations reveal that presented 3 T 1 R -PMs has large pose operation capability. This paper systematically develops the type synthesis of single-loop parallel mechanisms (PMs) with three translations (T) along three independent directions and one rotation (R) around one fixed direction (3 T 1 R -PMs). Each limb is driven by a multi-degree of freedom (DOF) drive system, and the output link can generate large rotational angle. Based on previously presented multi-DOF drive systems (DSs), a novel systematic method is proposed to synthesize single-loop 3 T 1 R -PMs based on Lie group theory. To improve the rotation function of the single-loop 3 T 1 R -PM, two types of connecting styles between the output link and the ends of two limbs are introduced to construct the single-loop 3 T 1 R -PM with a full circle rotation function. A class of single-loop 3 T 1 R -PM with two serial limbs driven by a 2-DOF driver and a class of single-loop 3 T 1 R -PM with a hybrid limb driven by a 3-DOF DS and a serial limb driven by a 1-DOF joint are constructed. Moreover, the simulations are implemented to display large pose operation capability of two examples of presented 3 T 1 R -PMs. [ABSTRACT FROM AUTHOR]