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In the field of robotic assisted rehabilitation, some parallel mechanisms guide the anatomic limb using a kinematic chain (similar to an exoskeleton), thus, the motion of the moving platform serve no benefit in controlling the rehabilitation exercise. However, the dependency between the active joints of the robot and some intrinsic motion parameters (correlated with the anatomic joints) is required. The authors propose a new algebraic parameterization method based on Study parameters of SE(3), which achieves a direct mathematical description between the desired motion parameters of parallel mechanisms. The moving platform coordinates are eliminated from the constraint equations together with unwanted motion parameters (usually free motion parameters). The approach is first demonstrated on a generic mechanism and thereafter, in a case study, where the constraint equations are derived for a parallel robot (RAISE- designed for lower limb rehabilitation) by eliminating the free motion parameters and obtaining simple input/output equations relating the motion of the active joints of the robot with the motion of the hip and knee joints. The forward and inverse kinematics are presented with numerical examples. The singularities and workspace are also determined for the RAISE parallel robot, showing the particularities and advantages of the proposed approach.

Compared with conventional parallel manipulators with serial kinematic chains supporting a nonflexible platform, generalized parallel mechanisms may be further constrained by interconnected coupling sub-chains or configurable platforms. The additional coupling sub-chains and configurable platforms have the potential advantages of improving overall characteristics and executing specific output motions. Based on the applications, this paper proposes a symmetric generalized parallel mechanism with so-called Schonflies motion. This mechanism can generate three independent translations in conjunction with a partially decoupled rotation which refers to a given direction. To improve the dynamic performance, all the actuators are installed on the fixed platform. The paper starts with the number synthesis of independent loops that can derive all possible non-isomorphic contracted graphs of the 3T1R generalized parallel mechanism. The threefold-symmetric Bricard linkage is introduced into the generalized parallel mechanism. Besides, several novel generalized parallel mechanisms with various motion patterns are provided. The kinematic analysis of the proposed architecture is established. The evaluation of the workspace is conducted. Finally, the study of the overall Jacobian matrix is performed and the singularity including kinematic singularity and constraint singularity is analyzed.

Capturing non-cooperative targets in space is a cutting-edge technology in the aerospace field. In this study, a novel n(3RRlS) metamorphic serial-parallel manipulator (MSPM) with multiple working conditions is proposed, which can serve as the fingers of a large-scale reconfigurable space multifingered hand (LSRSMFH). First, a limb combination coding method is proposed to describe the topological graph and determine the isomorphism of the n(3RRlS) MSPM. Subsequently, the topological graphs and the limb combination codes (LCCs) of the 1(3RRlS) MSPM, 2(3RRlS) MSPM and 3(3RRlS) MSPM are further analyzed, and the isomorphism of all the actuation distribution configurations (ADCs) and metamorphic configuration states (MCSs) is determined. Second, a two-actuator method is applied for the n(3RRlS) MSPM, and the workspaces of all MCSs of all ADCs of the 1(3RRlS) MSPM, 2(3RRlS) MSPM and 3(3RRlS) MSPM are analyzed using a transformation method. The results show that the n(3RRlS) MSPM can realize their respective functions of the LSRSMFH under three working conditions with the minimum number of actuators, which can reduce the number of actuators and the weight of the LSRSMFH and can gain benefits in multitask adaptability, simplified control, precision and rigidity improvement, energy saving and risk reduction.

A three-dof 2 P UR-2R P U redundantly-actuated parallel-kinematics machine, designed for the machining of complex curved surfaces that require high-speed and high-precision, is the object of study in this paper. The lower-mobility PKM, consisting of two pairs of symmetric, limited-dof limbs, has the advantages of high stiffness, simple kinematic chain, and reduced singularities. The mobility of the robot is investigated via Lie-groups, instead of the well-known Chebyshev–Grubler–Kutzbach formulas, which are not applicable to our case. Then, the inverse-displacement, direct-displacement and corresponding velocity relations are analyzed in detail. Next, by investigating the rank-deficiency of the corresponding Jacobian, three types of singularities, those associated with direct-kinematics, inverse-kinematics and combinations thereof, are analyzed in depth, while constraint singularities are investigated by resorting to constraint wrenches. Moreover, the workspace of both the reference point P and the tool head, when a tool is added to the moving platform, are derived. It is noteworthy that the local and global dexterity indices are evaluated by resorting to the characteristic length to homogenize the dimensionally inhomogeneous Jacobian matrix at hand, then the condition number is minimized over the independent posture parameters and the characteristic length via the first-order normality conditions.

In this paper, we present a new transmission index (TI) for kinematic performance evaluation of a class of parallel manipulators with a 3-RS (or 3-SR) structure; termed the primary structure obtained by locking all actuated joints in the manipulators. TI is based on the pressure angle that is defined in a kinematically equivalent structure, a 6-SS structure by replacing an RS chain of the primary structure with a pair of SS chains, which can reflect the practical force transmission and constraint characteristics of R joint composed of two bearings in the original manipulator. The effectiveness of TI is verified by considering 3- P RS and 3-R P S parallel manipulators. The singularity analysis, relationships between the maximum joint forces and index values, distribution of TI inside the workspace, and an application of TI to a kinematic design are demonstrated. The proposed approach can indicate both output and constraint singularity conditions with a single index, can be achieved by simple calculation process without complicated normalization, and can include the width of the revolute joint in the kinematic performance evaluation of this class of parallel manipulators.

Walking machines may be used for both walking and manipulation objectives. A walking robot can walk to a target and then do manipulation. For the manipulation objectives, hexapod robots are potential solutions as they show intrinsic stability in addition to providing six degrees of freedom to the top platform. On the other hand, when the robot does in-situ manipulation without walking, it has a confined workspace due to its parallel structure. This paper presents how to design a radially symmetric hexapod walking robot to achieve the maximum possible workspace when a limited size of the robot is intended. After an analytical characterization of the workspace, an optimization algorithm is used to calculate a set of kinematic and structural parameters with which the maximum reachable workspace is theoretically guaranteed given a desired size of the robot. A prototype of the robot is fabricated based upon the calculated parameters to experimentally test and measure the reachable workspace of the robot. The results confirm that the robot achieves the maximum workspace as far as physical constraints allow. It is also shown that the stability consideration of the robot constrains the reachable workspace of the hexapod robot.

The aim of this paper is to give a detailed examination of the input and output singularities of a 3- R UU parallel manipulator in the translational operation mode. This task is achieved by using algebraic constraint equations. For this type of manipulator a complete workspace representation in Study coordinates is presented after elimination of the input parameters. Both, input and output singularities are mapped into a Study subspace as well as into the joint space. Therewith a detailed singularity investigation of the translational operation mode of a 3- R UU parallel manipulator is provided. This paper is an extended version of a previous publication. The addendum comprises the discovery of a possible transition between two operation modes as well as a self motion and an examination of another component of the output singularity surface, most of them for arbitrary design parameters.

The generalized parallel mechanisms (GPMs) become a new feasible research topic to explore the advantages and overcome the shortcomings of the traditional parallel mechanisms (TPMs). This paper aims to address the challenge of the synthesis method for the GPMs with large rotational angles and integrated end-effectors (or configurable platforms). A sufficient condition for the independent rotations is presented and a design framework for constructing independent rotational degree of freedom (DOF) is developed. Using the set mapping and the Lie group theory, a method for synthesizing GPMs with hybrid structures is proposed on the basis of the obtained sufficient condition and the design framework. This method provides a way to connect the symmetric 0-DOF closed-loop kinematic chains with the parallel limbs to preserve the motions of both the parallel limbs and the elements in the closed-loop chains. A 3T3R GPM with 3-dimension large rotational angles and a class of 4-DOF and 6-DOF GPMs with 1-DOF integrated end-effectors are synthesized using the proposed method. The orientation workspace of the example GPMs are analyzed and discussed to reveal the high rotational capability. The obtained GPMs are suitable for the occasions that require high rotational performance, assembly, pick-and-place, drilling and other industrial applications.

Spraying robot is a kind of important industrial equipments. However most of them cannot flexibly change their workspace. In order to obtain a spraying robot with extremely large workspace but a small storage space, we synthesize an innovative mobile robot with a telescopic forearm. First, the structure of a four-side deployable arm to generate straight line motion for the mobile robot is proposed. It adequately enlarges the workspace and reduces the storage space because of the stretchable structure. Based on the new structure, the homogeneous transformation matrix and Jacobian matrix of the forward and inverse kinematics are deduced in details for workspace evaluation. Geometry analysis indicates that the four-side deployable structure effectively extends the arm of the robot, and therefore it has much larger workspace than its existing counterparts do.

This paper presents the design exploration of robotic hands so as to achieve maximum precision manipulation workspace. Kinematic workspace of the hand depends on the object being grasped; therefore we refer to the workspace as the hand-object system workspace. We have considered a three-fingered hand and a tripod grasp on a cylindrical object. We discuss the effect of design variation by changing the finger base location and finger link lengths. Fully actuated and under-actuated versions of the hand have been considered. The workspace has been analyzed in terms of kinematic position and orientation workspace. Results show that for fully actuated hand and large object size, hand designs with finger base farther apart give a larger workspace. For small size objects, however, hand designs in which finger bases are closer together give a larger workspace. Under-actuated versions of the hand give a larger workspace for designs with finger base farther apart, for both small and large object size. Longer link lengths give larger workspace in case of both large and small objects.

Self-adaptation is a typical and widespread characteristic in underactuated finger grasp. This paper presents the self-adaptive grasp process and equilibrium configuration of a 3-DOF underactuated finger comprising cable-truss units, which uses a tendon-pulley transmission and parallel four-linkage mechanism to realise grasps. The structure and the self-adaptation at the grasp closing stage are illustrated. On the basis of a situation where one or two phalanges are in contact with the object, fixed-point grasp models and the joint workspaces are discussed, respectively. The corresponding workspace that is formed when the distal phalange contacts the object at a fixed point is assessed through numerical analysis. The expression of general static contact force is established by using the virtual work principle, and expressions reveal that the phalanges’ static statuses are obtained. According to the middle phalange contacting or not contacting with the object, the distributions of every phalange condition are assessed, and the self-adaptive grasp process in complex distribution regions and four equilibrium grasp configurations are analysed from two grasp situations. Valid and adequate self-adaptive grasp experiments are conducted to verify the accuracy of the self-adaptive grasping analysis.

A novel 3-degrees-of-freedom (DOF) spherical mechanism, singularity-free in the anatomical shoulder joint workspace, is described. The use of curved scissors linkages interconnected by revolute joints, whose axes share the same remote centre-of-motion, achieves the most compact design of its kind. The kinematics of this scissors shoulder mechanism (SSM) are derived and presented. A design equation restricting the linkage's curvature by the central/pitch angle of the fully stretched scissors is obtained. Motion-captured data are used for validating the reachable 3-d workspace while a test-subject is wearing a null protraction/retraction constrained exoskeleton. The embodiment of the SSM as a shoulder joint for an exoskeleton device does not compromise the upper extremity function within the anatomical reachable 3-d workspace. It operates within a volume of 0.236 m3, corresponding to 68.09% and 94.97% of the volumes of the full active (0.350 m3) and null protraction/retraction constrained active (0.223 m3) reachable workspaces of the test-subject, respectively. Thus, the SSM represents a simplification of a spatial spherical mechanism design and overcomes the need for the use of redundant links and optimization routines.

Although additive manufacturing (AM) has been developed rapidly and become an absolutely necessary tool for reducing the cycle and cost of new product development, the mechanical structures of most 3D printers based on Fused Deposition Modeling (FDM) technology are still traditional serial or parallel mechanisms with rigid components. In this paper, a novel cable-driven parallel 3D printer (CDPP) is developed. Compared with the traditional rigid mechanisms, CDPP has the advantages of larger workspace, higher payload-to-weight ratio, easier modularity and reconfigurability. A cable-driven module with three translational degrees of freedom and a follow-up tensioning module with a spring are adopted for positioning. Firstly, the inverse kinematics of the CDPP is derived considering the cable length constraint. The inverse dynamics model of the CDPP is established based on the Newton–Euler equation and the kinematics. Secondly, the system stiffness of the CDPP and stiffness along three coordinate axes are derived, respectively. The system static stiffness with respect to the stiffness constant of the spring and the coordinates of the moving platform are obtained. Finally, the experiments are performed based on numerical simulation. The results of experiments without executing extrusion demonstrate the simulation results about the static stiffness. The feasibility of the CDPP is verified via the experiments while executing extrusion.

This paper introduces the concept of isomorphism into the study of metamorphic mechanisms and presents the design of the isomorphic metamorphic mechanism, in which the structure is the same but the shape topology is different. A novel plane-space polyhedral metamorphic mechanism governed by the edge forming principle is developed. This mechanism is able to achieve the structural transformation between plane topology and space topology, and it has broad prospects for engineering application. The polyhedral metamorphic mechanism can be evolved into isomorphic mechanisms, like the spherical metamorphic mechanism and conical metamorphic mechanism, according to the scale relation between links. The evolution principle and movement conditions of the isomorphic mechanism are analyzed. The position and velocity of joints of novel plane-space isomorphism metamorphic mechanism and the workspace of these mechanisms are compared and analyzed using screw theory, and the configuration expanded analysis of novel plane-space metamorphic mechanism is performed. Finally, potential engineering applications are listed. The research results provide a reference for the reasonable choice of application configuration for such mechanisms.

Due to the complex dynamic characteristics of a hybrid spray-painting robot, the motion accuracy fluctuates in the workspace. In order to reduce the accuracy fluctuation of the hybrid robot, this paper proposes an engineering-oriented motion accuracy assurance method by considering dynamic characteristics, including workspace optimization and control parameters design. First, the dynamic model of the hybrid spray-painting robot is derived based on the virtual work principle, and a dynamic evaluation index is investigated to describe the possible maximum dynamic load. Then, based on the evaluation index, the relative location of the task workspace for painting an aircraft wing in the whole workspace is optimized. Then, a control parameters design approach is presented to ensure that the robot always has desired accuracy in the optimized task workspace. Finally, some experiments are performed, and the results show that the robot has better performance in the optimized task workspace with the designed control parameters, which proves the effectiveness of the proposed method.

This paper presents the solution to inverse kinematics of a mobile manipulator operating in both obstacle free environment and cluttered workspace. This work conceives an optimization problem using bidirectional particle swarm optimization method to obtain the inverse kinematics solution of the mobile manipulator. The bidirectional search algorithm helps to search for the solution faster than conventional unidirectional search. The novel manipulator decoupling technique proposed in this paper enables the system to carry out bidirectional search to find inverse kinematics. Collision detection and obstacle avoidance tasks are undertaken using the algorithm proposed in this work to avoid line type obstacles. A multi-objective optimization problem is formulated with minimum total joint movement as another objective function and collision avoidance as constraint. Numerical are experiments performed on a four degree of freedom manipulator mounted over a mobile base to illustrate the efficacy of the proposed method.

Coordinates play an essential role in the description of real world objects and physical processes. In robotics, coordinates are used to describe the kinematic structure and the kinematic and dynamic behavior. The description mostly takes place in charts, assigned by the observer of the robotic system. However, it is crucial that the described physical process does not depend on the coordinate choice of the observer. In this work we show the relation between coordinates and manipulability analysis. Manipulability measures are dependent of joint coordinates of the robot and task coordinates in the workspace of the robot. Both relations can be analyzed with tensor geometry. We remove the dependency on joint coordinates through the use of an appropriate metric. With the help of tensor contraction, the resulting induced metric in the workspace can be transformed into a coordinate invariant matrix. After applying eigenvalue decomposition on this matrix, we can visualize the dynamic manipulability of a robot as a coordinate invariant ellipsoid.

The small workspace and complicated singularities severely limit the application of parallel manipulators. The methodology of redundancy is commonly used to eliminate singularity and enhance the kinematic performance of parallel manipulators. However, redundancy results in apparent drawbacks including intensified internal force coupling and complicated dynamic control. A new potential method to improve the kinematics and eliminate singularities, named actuation mode conversion, is investigated in this study. First, a planar 3-RRR parallel manipulator that can realize 27 actuation modes is designed. Based on the matrix orthogonal degree, indices for evaluating the transmission performance are defined, and kinematics of the 3-RRR manipulator under different actuation modes is analyzed. Results indicate that the actuation modes significantly affect the kinematic performance of the parallel manipulator. A reasonable selection of the actuation modes can effectively improve the kinematic performance of the planar 3-RRR parallel manipulator and eliminate type II singularities. Finally, dimensional parameters of the variable-actuated 3-RRR manipulator are optimized via the atlas-based method considering actuation mode conversion, and the optimal conversion map of the actuation modes is obtained.

An optimization method using Particle Swarm Optimization (PSO) is introduced in order to simultaneously optimize the trajectory planning and placement of a given path in a redundant coordinated robotic workcell. The workcell consists of a 6 Degree Of Freedom (DOF) serial manipulator, a 6 DOF parallel manipulator and a rotary table mounted on the parallel manipulator. Since the workcell has 13 DOF, one has to solve the kinematic redundancy of the workcell. The solution will be obtained considering the singularities of the serial manipulator and the workspace boundaries of all manipulators. The algorithm to obtain the optimum path placement is explained through a simple example and the result for a helix path around the workpiece is represented.

Accurate assessment of the robots’ stiffness is a difficult step in calculating the effect of the components flexibility on the accuracy and performance of the robots. This difficulty is sometimes resulted from the complex geometries of the flexible components of the robots. This paper proposes an exact analytical method for calculation of the robots’ stiffness which can be readily extended to all the robot types with complex geometries. The proposed method is based on the Castigliano's second theorem and calculation of the strain energies of the flexible components. This method significantly reduces the need for the simplifications commonly made in the modeling of the stiffness matrix of the robots. Unlike the traditional methods, the proposed method can consider the effects of the distributed loads applied to the robot and the distributed weights of the components. Moreover, the bending moments, shear forces and torsional moments applied to each component of the robot can be considered. The robot's structure is modeled as a distributed system and the position error of the end–effector is calculated as a function of the flexibility of all bodies and joints. Next, a parallel robot with 3–RUU kinematic chain is considered as a case study. Using the concept of Wrench Jacobian Matrices (WJMs), the internal wrench of each flexible component is calculated. The internal wrenches are obtained, for all the robot's configurations over its entire workspace, as functions of the external wrenches applied to the end–effector and distributed weights of the robot's moving bodies. The WJMs are used to calculate the compliance matrices of flexible components as well as overall compliance matrix of the robot. Using the overall compliance matrix of the robot and applying a computational algorithm, a comprehensive study is performed to evaluate the effects of the components’ flexibility on accuracy of the robot. Finally, the range of the total compliance error is calculated throughout the robot's workspace. The total error range is calculated according to the physical characteristics of the robot and allowable range of the external wrenches applied to the end–effector. For this purpose, a general compliance error range (GCER) is defined throughout the robot's workspace. The GCER defines accuracy interval of the robot's end–effector with respect to the flexibility–induced errors of compliant modules.

Performance indices are extensively used in the optimization of robot structures. However, in the case of manipulators with mixed translational and rotational DOFs, traditional indices are not readily applicable due to the non-homogeneity of the Jacobian matrix. In this paper, special cases of generalized inertia ellipsoid, GIE, [1] and rms velocity norm [2] are used to define a payload specific performance index based on the transferred kinetic energy to the payload. The proposed kinetic energy index, KEI, is dimensionally homogeneous and is independent from the units. Moreover, this index is scale invariant and simultaneously considers both of the translational and rotational motions. A unit KEI indicates that a uniform kinetic energy is transferred to the payload for all the feasible joint velocities. For better representations, kinetic energy ellipsoids are drawn using a new vector form definition of the kinetic energy. A two-link manipulator and a 3- R RR robot are considered as case studies for evaluation of the proposed index. The kinetic energy ellipsoids and contours of KEI value are plotted over the entire workspace of the two robots. For a given payload with specified dynamic characteristics, KEI can be used to design an optimal structure of the manipulator such that a uniform kinetic energy is transferred to the payload.

The avoidance of singularities is critical to design and control of parallel robots. This paper aims at efficient determination of the maximal singularity-free joint space and workspace of a class of six-DOF parallel robots with six kinematic chains of same type. We represent the singularity-free joint space by a 6-cube and determine it firstly. The singularity-free workspace is generated by continuous motion of all active joints in the singularity-free joint space. As a result, the boundary of the workspace can be obtained with simultaneous consideration of position and orientation of the mobile platform. The size relation between the maximal singularity-free joint space and workspace is discussed. To efficiently determine the singularity-free joint space and workspace, we propose dual quaternion-based Jacobian matrices and construct an efficient algorithm. The algorithm detects singularities in a given joint space and simultaneously calculates its corresponding workspace. The computational costs of the proposed algorithm and the traditional one are compared using a 6-U P S parallel robot, leading to 9 seconds and 458 seconds respectively. Finally, both the maximal singularity-free joint space and workspace of a 6- P US parallel robot are determined to further demonstrate the effectiveness of the new approach.

This paper presents a new remote center of motion (RCM) mechanism design for Minimally Invasive Surgery (MIS) robotic manipulators, capable of providing two important degrees of freedom (DoFs) — pitch and translation — purely through its mechanism design. Novelty of the proposed design is that it offers a significantly smaller footprint compared to the existing state-of-the-art 2-DoF planar RCM mechanisms. We describe the design, perform kinematic analysis, and use simulation to validate its RCM capability. The design is also optimized using manipulability and tool translation to achieve maximum kinematic performance with smallest size of the proposed mechanism. A comparison between the mechanism workspace and the required workspace shows that the proposed design meets the MIS workspace requirements. Optimization results demonstrate that the proposed design offers same kinematic performance as of an exiting design, but with a significantly smaller footprint. Compact distal-end and smaller footprint make the proposed design ideal for applications requiring multiple manipulators to operate in close proximity.

This paper deals with the dynamic stability problem of a tripod parallel robotic wrist by means of monodromy matrix method. This robotic wrist can generate a continuous end-effector rotation in any configuration within its orientation workspace, which allows the manipulator to function as a machine tool head used for a drill point grinder. The system’s linearized equations of motion are established in terms of both lateral and torsional vibrations to analyze the stability problem, resorting to the Floquet theory. As a result, the stable regions of the manipulator are visualized, and the stability charts are constructed on various parameter planes to detect the parametric instabilities and to reveal the effect of the selected pairs of system parameters onto the stability. Critical parameters, such as the rotating speeds of the driving shaft and the actuation stiffness, are identified for the prototyped grinder.

In this paper, dynamic performance and workspace of four cable layouts of a parallel robotic marine platform (PRMP) are analyzed. The four cable layouts are called 3-3, 6-6, 6-3, and 3-6 PRMPs. There are six-degrees-of-freedom (DOF) cylindrical floating structures and twelve cables anchored to the seabed. Their workspaces are identified with/without the effects of the environmental loads. In order to provide necessary motion to compensate the environmental loads, cable tensions are applied to keep the floating platforms rigid while they move horizontally due to the environmental loads. The PRMPs are analyzed in the framework of rigid-body dynamics. This work aims to improve the performance of the PRMPs.

2-DoF rotational mechanism is increasingly utilized in a large range of industrial applications. However, the structures of most of the existing mechanisms are very complex, which is a significant challenge for building them, due to the tight tolerance and assembly difficulties. In this paper, a class of 2-DoF tendon driven parallel kinematics mechanisms (TDPKM) are introduced, which can be structured with low manufacturing and assembly difficulties and is able to actively adjust the system stiffness. Since the unique class of mechanisms is developed, the kinematic model is established to derive the stiffness model, which considers the tendon, structural and central joint stiffness. Finally, a set of experiments of the deviation measurement under different payloads within the workspace are implemented and compared with the theoretical calculations presented in this paper. The overall deviation error between the experimental test and theoretical calculation are between 0.9% and 4.7% in the whole workspace.

This paper addresses the isotropy of a workspace in terms of its geometric shape. Workspace isotropy analysis plays a crucial role in improving the quality of workspace for parallel manipulators. When a parallel manipulator is installed on a moving platform (e.g., satellites, aircrafts, ships, etc.), the geometry of its workspace is critical to achieve the planned tasks. This paper proposes three novel workspace isotropy indices, namely, translational workspace isotropy index (TWII), rotational workspace isotropy index (RWII), and entire workspace isotropy index (EWII), for workspace isotropy analysis in terms of the geometric shape of the workspace. All three indices are mathematically defined. TWII and RWII can be applied to both planar and spatial parallel manipulators with movable bases while EWII can work for planar parallel manipulators with movable bases. Random rotational disturbances are applied to the movable bases of multiple parallel manipulators in simulation. Simulation results show that the proposed workspace isotropy indices are effective in evaluating how isotropic the geometric shape of a workspace is. They are good at reflecting the robustness of a parallel manipulator to rotational disturbances to its movable base. The proposed indices can also be used as guidelines for the optimal design of parallel manipulators.

Parallel robots feature several favourable properties, including the potential for high acceleration and accuracy. However, in order to minimise cycle times and optimise the usage of factory space, industrial applications commonly include multiple closely mounted robots, working on the same or closely located objects. As parallel robots generally suffer from a limited workspace-to-footprint ratio, attempting to utilise parallel robots for such applications typically leads to issues with mechanical interference. This paper investigates the feasibility of dividing a planar workspace into several smaller areas, each of them serviced by a dedicated planar parallel mechanism. Applications where this arrangement could be beneficial include 2D manufacturing operations, such as water jet cutting and laser cutting. Additionally, the proposed arrangement could be extended by actuating either the work object fixture or the entire array of mechanisms in one additional degree of freedom. The resulting architecture could be beneficial for 3D manufacturing operations, such as additive or subtractive manufacturing. The presented analysis studies the limitations of such architectures in terms of mechanical interference and achievable kinematic performance. Solutions to reduce mechanical interference are introduced and screw-theory-based indices are employed to evaluate the achievable kinematic performance.

It is well known that there exist interior barriers within the boundaries of the workspace of redundant robots. These interior barriers, which are drastically affected by kinematic constraints, are very important for trajectory planning since they imply motion impediments for the robot. Existing geometrical and singularity-based methods that obtain such interior barriers cannot accommodate complex (yet common) kinematic constraints, such as the condition that collisions between different links should be forbidden. This paper presents a new sampling method to obtain the boundaries and interior barriers of the workspace of redundant robots considering collision constraints. The proposed method identifies the occurrence of barriers with the vanishing of connected components of self-motion manifolds. Our method consists of three phases: (1) densely sampling self-motion manifolds by solving the inverse kinematics, (2) clustering phase to identify disjoint self-motion manifolds, and (3) matching phase to detect the vanishing of self-motion manifolds. The presented method is illustrated with several examples involving redundant parallel robots, considering joint limits and collisions. These examples demonstrate the feasibility and usefulness of the proposed method, and illustrate the drastic changes suffered by workspace barriers due to collision constraints.

The main aim of this paper is the influence assessment of the one of the most significant non-geometrical errors called compliance errors on accuracy of a 3- P RUP parallel robot. In this paper, a detailed and comprehensive study is performed to evaluate the effects of the joints and bodies flexibility on position accuracy of the robot. For this purpose, a continuous modeling method based on the energy method and Castigliano's 2nd theorem is presented. The capabilities of this method significantly reduce the limiting assumptions to obtain a highly accurate analytical stiffness model. Using the capabilities of this method, the compliance errors modeling of flexible bodies with complex geometry will be possible as well as the bending and torsional moments, shear forces and weight of all robot compliant modules can be considered as continuous loads. Using the concept of Wrench Compliant Module Jacobian, WCMJ, matrix and physical/structural properties matrix of each module, the compliance matrix of each flexible module is independently obtained. Using a computational algorithm, a comprehensive study is performed to obtain the contribution of the joints flexibility on the robot accuracy throughout the workspace. Finally, to evaluate the compliance errors boundaries throughout the workspace, the concept of General Compliance Error Range, GCER, is presented. The GCER represents a range between maximum and minimum accuracy of robot relative to the compliance errors.

This paper presents a constant balancing 6UPS/(3PRRR)+S parallel mechanism. It is composed of two nested parallel mechanisms: the outer 6-UPS parallel mechanism and the inner 3-PRRR balance mechanism, both of which are connected by a spherical joint. Because the Jacobian matrix of the 3-PRRR balance mechanism is constant, the invariant balancing performance of the 6UPS/(3PRRR)+S parallel mechanism can be achieved by just keeping the input forces of the inner balance mechanism constant at any pose in the global workspace, which has brought great convenience for the application of these mechanisms with good balance characteristics. The dynamics model of the 6UPS/(3PRRR)+S parallel mechanism is established based on the screw theory and the influence coefficient method. Then the μ(balance coefficient) of the mechanism is defined, the balancing performance of this mechanism is analyzed by using the value of F ¯ (average driving force) under the condition of the same balance coefficient. The balancing performance of the 6UPS/6UPS parallel mechanism is compared with that of the 6UPS/(3PRRR)+S parallel mechanism under the condition of the constant input force of the balance mechanism and the constant balance coefficient, consequently, the comparative result proves the excellent global constant balancing performance of the 6UPS/(3PRRR)+S parallel mechanism.

The 3- C CC class of parallel-kinematics machines (PKMs) bears many interesting features, as found in a previous paper on its optimum design. In this paper, its forward-kinematics (FK), singularity, workspace and dexterity analyses are studied. FK reveals that the rotation and translation of the moving platform (MP) are decoupled at the displacement level; moreover, a simple formulation is derived for the orientation subproblem that admits up to eight solutions, which is minimal; a quartic resolvent polynomial for the FK is then derived. All solutions thus can be found simultaneously in closed-form, while the computational cost is reduced; this brings robustness, especially when the robot operates near a singular configuration. Next, the translation problem is solved from a linear-equation system. These features, rare in six-dof PKMs, greatly simplify its simulation and control. Next, the singularity in question is shown to be determined solely by the orientation of the MP, thereby simplifying dramatically its evaluation and representation. Furthermore, the robot is shown to bear position and orientation workspaces of reasonable size, together with high dexterity. These features make the proposed PKM class quite promising in a variety of applications.

This paper presents the design, optimization, fabrication and testing of a new piezo-driven compact XY parallel stage for nanopositioning applications. A decoupled, compact parallel stage is developed by a stacked design, which provides a larger area ratio than existing piezo-driven stages. Displacement amplifiers are adopted to amplify the stroke of piezoelectric actuators. The amplifiers are then improved and integrated with the motion decoupler to isolate the two actuators. The main design variables of the stage are optimized by applying a genetic algorithm based on finite-element analysis (FEA) to achieve the required performance. The optimized design is then further improved to enhance the stage performance, which is verified by performing FEA simulation studies. A prototype stage is fabricated for experimental study. Both open-loop and closed-loop testing are conducted to validate the stage’s performance. Results show that the decoupled XY stage possesses a compact dimension of 87.2 × 87.2 mm2, which offers a workspace of 212.48 × 219.24 µm2 with a resolution of 7 nm.

Dynamic performance evaluation is an open question considering three main challenging issues: (a) how to avoid performance indices physically inconsistent considering different dimensions of translational and rotational performance of parallel robots; (b) how to accurately evaluate the performance of the whole robots considering different capacity of driving motors, active arms and moving platforms; (c) how to understand the inner relationship between the dynamic performance and parameters of robots. In this paper, through matching the driving system with the parallel mechanism, an acceleration capacity index of the whole robot is proposed for high-speed parallel robots with mixed types of DOFs (translations and rotations). From the view of power transmissibility, the comprehensive interaction mechanism of motion/force transmissibility to the acceleration capacity of the robot is analyzed and presented in the proposed index. Thus, the index can measure the acceleration capacity accurately. For validation purpose, this index is applied to acceleration capacity evaluation of a high-speed parallel robot, identifying a suitable workspace to reduce the driving torque. This index is general and can be further applied to parameters optimization for different types of high-speed parallel robots.

Singularity is a fundamental problem in robotics which seriously affects the motion control, path planning, and off-line programing of the robot. In this paper, the singularities of a 7R 6-DOF painting robot with non-spherical wrist are analyzed in detail, and a new avoidance method is proposed. Firstly, the singularities are decoupled into the position singularities and the orientation singularities by introducing a virtual wrist center. All singularity conditions for both cases are identified based on a rational transformation between the 7R 6-DOF robot and the equivalent 6R robot with spherical wrist. Secondly, the position singularities are regarded as inescapable singularities, and unusable regions are defined in the workspace to deal with these singularities. Thirdly, the orientation singularities are regarded as escapable singularities. Based on the definition of functional redundancy for painting application, the Twist-decomposition approach (TWA) is extended to handle the orientation singularities. As the main improvement, a new and simple singularity criterion is proposed to overcome the drawback of the existing algorithm. In the end, two simulations for a 7R 6-DOF painting robot are implemented to demonstrate the effectiveness of the proposed method.

This paper revisits some fundamental issues in kinematic analysis of spherical parallel robotic manipulators (SPRMs), such as the orientation capacities of the mobile platform (MPF), and assembly modes determination. The orientation capacities are analyzed by using several types of workspaces: total orientation workspace, full-spin orientation workspace, and constant-spin orientation workspace. The adopted representation of the MPF orientation brings up-to-date the use of the spherical coordinate system, which we find more appropriate when Euler angle orientation parameters are used. This representation is applied to each limb, considered independent from the rest of the mechanism and having the mobile platform as end-effector. The 3D orientation space reached by each limb, which is called also vertex space, is represented as a 3D solid volume. Thereafter, the operational space of the SPRM is directly determined by the Boolean intersection of the previously obtained volumes. Moreover, by fixing the joint space variables, the domain reached by each limb in the operational space is a surface. The Boolean intersection of the obtained surfaces is nothing but the set of points corresponding to the solutions of the forward kinematic problem. These operations are implemented in CAD software and the proposed approaches have been validated successfully by using several examples of application for both workspace determination and representation and FKP resolution.

This paper presents an asymmetric fully constrained parallel mechanism prototype that has three rotation degrees of freedom and three actuations. The mechanism employs pantographs as three-rotation constrained leg instead of normal RRR-leg to avoid disadvantages like singularity, uncertainty or interference with other legs. Reciprocal results based on Grassmann geometry are categorized, and used for analyzing surfaces whose Jacobian matrix determinant is zero. Angle derived from reciprocity is used for its straight geometry meanings. Larger angle would push singularity away from workspace and has maximum value of 90°. The results showed that the design has desired freedoms, and angle has monotone increasing relation with the determinant of Jacobian that could avoid singularity and afford a rapid way for future optimization.

This work presents a novel soft actuator with a 3D-printed elastic body based on a fused-deposition-modeling technique and with tendon actuation based on flexible shafts, which allow push, pull, and twist torque transmissions. The combination of the soft body and flexible shaft furnishes an easy-making, modular and functional unit that possesses softness and enables three degrees of freedom. We derive the kinematics and statics of the actuator based on the assumption of piecewise constant curvature, and identify the parameters experimentally. To understand the performance of the soft actuator in different design and fabrication settings, extensive experiments are performed to compare different shapes of cross sections, infill densities, infill patterns, dentation structures and moment arms in terms of generating forces under the same pulling forces. In addition, experimental validations are performed to characterize other properties such as workspace, hysteresis, pushing force, transmitted torque, and tip force under both bending and twisting. Finally, three potential applications, i.e., a soft robotic hand, a multisegment continuum robot, and a miniaturized drilling device, are prototyped and presented experimentally where the flexibility endowed by the shafts is demonstrated and highlighted. The scalability and modularity are also showcased in the three applications.

This paper deals with continuous path motion planning of a spatial 3-DoF cable-suspended parallel robot considering the robot’s dynamic constraints. First, based on the analysis of the algebraic and geometric properties of cable tension constraints, we present the sufficient and necessary conditions for the end-effector to pass through parallel singularities along straight line paths. Then, a piecewise linear interpolation method is introduced, showing that any target points above cable exit points can be connected in sequence via some intermediate points in the static workspace of the mechanism. The intermediate points are properly selected to avoid collisions between cables and obstacles, and the resulting trajectory is modified using quintic polynomials to enhance the performance. Afterwards, conditions for a general planar curve determined by three points to be feasible are given, and a general curve interpolation method is presented. Finally, three types of periodic trajectories are designed. Using the proposed trajectory planning method, not only can the positive cable tension constraints be satisfied, but the safety and the continuity of tensions can also be ensured. The effectiveness of the method is examined through simulations and experiments.

Parallel robots that incorporate kinematic redundancy in their designs are frequently considered for use in different applications due to their ability to avoid direct kinematic singularities within their workspace. Knowledge of a robot’s wrench generation capabilities constitutes essential information when designing its geometry and planning its optimal use to accomplish various tasks. In the presence of kinematic redundancies, the determination of a robot’s wrench generation capabilities at a given pose of its mobile platform depends not only on the limits of its actuators but also on the configurations of its legs. In this work, an algorithm allowing for the closed-form computation of the available wrench set of the 3- RP RR planar parallel robot is presented. This results in generating the boundary of the available wrench set as a set of faces in the wrench space. Based on this representation, algorithms allowing for the computation of various application-based performance indices are also described. Example numerical results are included to demonstrate how the tools that are presented could be used in the context of robot design.

Despite the importance of grasp synthesis for autonomous robotic operations, its formulation for continuum robots (CRs) has yet to be investigated. This paper presents a grasp taxonomy and a synthesis approach for CRs. The proposed synthesis relies on an analytical model for grasping using CRs. The method is extended for the application of cooperative continuum robots (CCRs). To present a comprehensive formulation of the problem, both constant-curvature and Cosserat-rod models are adopted in the proposed grasp synthesis. A set of grasp quality measures are formulated for this study, in which a new quantitative grasp quality measure is introduced to reflect the limited workspace of CRs. Finally, two experimental grasp quality measures are introduced (i.e., path-following error and grasp success rate) to compare and assess the grasps using statistical tests. The effectiveness of the proposed methodology is shown through extensive simulations and experiments using single-segment tendon-driven catheters.

A novel 1T2R parallel mechanism (PM), applied in loading test of hydraulic support, is proposed, whose kinematic performance is studied in detail. The analytical expression of forward kinematic positions are derived by means of vector method. With the aid of Jacobian matrix, the singular configurations are investigated. The orientation capacity of end-effector is depicted through the azimuth and tilt angles. Using screw theory as the mathematical tool, this paper establishes the evaluation indices for motion/force transmission performance such as input transmission index, output transmission index and local transmission index (LTI). The definitions and calculation methods of good transmission orientation workspace (GTOW), regular transmission orientation workspace, and average transmission index in regular workspace are presented, respectively. Furthermore, the distributions of GTOW and the surface of LTI are plotted. Finally, the analysis results indicate that PU-RPU-UPS PM has good kinematic performances, which can be used as loading actuator of the new hydraulic support test-bed.

The functionality of a workspace is one of the most important considerations in planar parallel manipulators (PPMs) design. Dexterous workspace (DW) is the subset of the reachable workspace (RW) and it means that full rotational dexterity is preserved in every translational position in space. However, DW is impractical as PPMs cannot rotate a full 360° because of interference. This paper proposes a workspace called prescribed flexible orientation workspace (PFOW) that characterizes the orientation capability of PPMs. To optimize and compare 3 degree-of-freedom (3-DOF) PPMs, a normalized and unified performance characteristic index is built based on indices including PFOW, condition number, velocity, payload, stiffness, and transmission indices which plays a guiding role in the optimization process. The best configuration is obtained through graphical performance comparison. In general, this work presents the analysis of rotational dexterity of PPMs and provides a guidance for optimization and selection.

Taking into account that the velocity and acceleration limits of the end-effector are specified rather than the physical limits of the actuators in the design purpose of a robot, this paper proposes a novel method to evaluate the dynamic performance of the robot along joint-space directions. Based on the given ranges of end-effector velocity and acceleration in task space, the required torque along all joint-space directions are obtained based on the velocity term and the acceleration term in dynamic model, respectively. Furthermore, the actual torque range of each actuator is derived to produce the required torque along all joint-space directions. Considering all the effects of the acceleration term, the velocity term and the gravitational term, two global dynamic performance indices that reflect the minimum range of actuator torque and the ratio of the required torque range to the actual torque range in the whole workspace are presented. This method is validated by utilizing it to evaluate the dynamic performance of a novel 4-DOF parallel manipulator with translational and rotational motion for FSW. This method conforms with the design process of robotic manipulators and would be useful for optimum design, dynamic performance evaluation and actuator selection of a robot.

Lower extremity exoskeletons are often used as walking assistance rehabilitation robots for paralyzed patients. However, due to the requirement of crutches or other devices to maintain balance, the under-actuated exoskeleton has limited applicability. This paper aims to design a novel mechanism for the self-balancing lower extremity exoskeleton, which structurally consistent with the human anatomy and fully actuated with 12 DOFs. In this study, based on the human-centered design principles, a bio-inspired exoskeleton mechanism synthesis methodology is presented. The novel serial-parallel hybrid mechanism is designed based on a 3-DOF RCM hip mechanism, 1-DOF parallelogram-linkage knee mechanism, and 2-DOF decoupled parallel ankle mechanism. To describe the forward and inverse kinematics of the mechanism, the closed-form solutions by the D-H method and geometric method are obtained, respectively. In addition, to analyze the exoskeleton workspace, the reachable workspace equations in the double foot support and single foot support phases are established. The numerical simulation and experimental results show the kinematics model validity and self-balancing walking ability, which illustrate the feasibility of the proposed exoskeleton mechanism.

Aiming at a 5-DOF hybrid optical mirror polishing robot, the explicit dynamic model considering the joint friction is established and the inertia coupling distribution is studied. Firstly, the kinematics of the manipulator is solved based on closed-loop vector method, and the dynamic model is established with Newton-Euler method based on the force analysis of manipulator components. Secondly, the kinematic parameters of the reference point of the moving platform are selected as the intermediate variables, and the explicit dynamic model of the parallel manipulator is obtained by parameters substitution considering the friction effects of spherical joints, universal joints and ball screws. Finally, on the basis of the dynamic model, the inertia coupling strength evaluation index for active branched-chains is proposed, and the distribution law of the coupling strength in a certain trajectory and workspace is studied. The results show that the inertia coupling strength indices between active branched-chains vary with the manipulator position and are symmetrically distributed in the workspace. This paper provides a theoretical basis for the joint controller design and structural parameter optimization of the polishing robot.

The complex structures, small workspaces and complex control systems of traditional parallel mechanisms are the largest hurdles to using them as leg mechanisms in walking robots. This paper synthesizes a family of novel 3-degrees-of-freedom (DOF) parallel leg mechanisms (PLMs) that have the potential to avoid these drawbacks. The novel parallel leg mechanism consists of a 3-DOF drive system (DS) and a walking mechanism, which can be designed modularly. Using the motion characteristics of the 3-DOF drive system, a simplified method for constructing 3-DOF parallel leg mechanisms is presented. Then, satisfactory 2-DOF walking mechanisms are synthesized based on Lie group theory. A family of novel 3-DOF parallel leg mechanisms in which the workspace of the foot-endpoint is a three-dimensional volume is constructed using the 3-DOF drive systems and 2-DOF walking mechanisms. Finally, the performance of the novel parallel leg mechanism is analysed, revealing the potential merits of this novel parallel leg mechanism in walking robots.

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.

© 2017 Elsevier Ltd This work addresses the inverse kinematic problem for redundant serial manipulators. Its importance relies on its effect in the programming and control of redundant robots. Besides, no general closed-form techniques have been developed so far. In this paper, redundant manipulators are reduced to non-redundant ones by selecting a set of joints, denoted redundant joints, and parametrizing its joint variables. This selection is made through a workspace analysis which also provides an upper bound for the number of different closed-form solutions for a given pose. Once these joints have been identified several closed-form methods developed for non-redundant manipulators can be applied for obtaining the analytical solutions. Finally, particular instances for the parametrized joints variables are determined depending on the task to be executed. Different criteria and optimization functions can be defined for that purpose.

The payload capacity of robotic manipulators is often considered to be the same throughout their workspace. However, the actual capacity largely depends on posture, velocity, acceleration and actuator limits. This work studies a method to increase the payload capacity of manipulators through trajectory optimization. This optimization is performed on a task basis and therefore, the load-carrying capacity varies from one task to another. Although the studied method is general and is not limited to specific robot architectures, an analysis of the method is conducted based on its application to a planar RR serial manipulator in a vertical plane. This manipulator is the most appropriate as a simple test case because most manipulators are built in such a way that most of the vertical motion of the manipulator is done by two parallel revolute joints: planar RR mechanism. Simulation and experimental results show that the payload capacity can be greatly increased compared to nominal values. It is also shown that, although the trajectories produced are not time optimal, the method is much more versatile and much simpler to implement than some other optimal control methods. The accompanying video provides a summary of the method and the results.