Parallel Kinematic Chains Research Articles

Manufacturing Technology, Experimental and Numerical Analysis of Static Bending of Three-Layer Composite Plate with Honeycomb Structure

The use of thin-walled constructions with honeycomb structure manufactured using additive technologies has several advantages compared to the constructions manufactured using traditional technologies. First of all, this is explained by the fact that additive technologies greatly simplify the production of honeycomb structures. A technology for manufacturing a three-layer composite plate with a honeycomb structure obtained using additive technologies is proposed in the paper. PLA plastic was chosen as the material for the honeycomb structure production. Printing was carried out using a "Delta" printer with parallel kinematic chains using FDM technologies. The printing temperature was 215 °C, table temperature – 60 °C. A fundamentally new scheme of an experimental plant for studying the bending of a three-layer plate is proposed. The aim of the research is to conduct tests of samples of a three-layer honeycomb panel for static bending when one edge of the sample is rigidly pinched. For the tests, a certified TiraTest 2300 universal testing machine (UTM), which allows to perform tensile and compression tests at a given traverse speed and measure the load with a relative error of 1%, was used. The UTM allows to load the sample and measure the load and displacement of the traverse. A sixteen-channel strain gauge station is used to measure the surface deformations of the housings. Transverse displacements of a three-layer plate were obtained as experimental data. The bending of the three-layer plate is modeled in the commercial package ANSYS. The results of experimental and numerical analysis coincide well.

On the methods of analytical mechanics for mathematical modeling of the dynamics of non-free systems and some variants of their application to the dynamics of parallel manipulators

The level of development of actuator technology and the element base and software of control loops of modern automatic devices makes it possible to use in technical practice complex control algorithms based on the results of mathematical control theory, including with incomplete information about the state. The effectiveness of such algorithms is determined by the presence of an adequate mathematical model of the device under study. For such a widespread class of automatic devices as manipulators with parallel kinematics, the problem of developing methods for creating mathematical models that allow taking into account nonlinear effects, despite the efforts of numerous researchers, remains relevant. To a large extent, the complexity of modeling the dynamics of this class of automatic devices is associated with the presence of parallel kinematic chains, which leads to the need to apply the results of analytical mechanics of non-free systems. In this section of theoretical mechanics, several rigorous methods have been developed, as a result of which mathematical models of different dimensions are obtained with different levels of complexity of the algorithms for their derivation and study. This leads to the need for a critical analysis of both the methods themselves and their possible application in technical practice. In this paper, the main algorithms for obtaining mathematical models of the dynamics of systems with geometric constraints are presented in detail and some comparative analysis of their application to modeling the dynamics of manipulators with parallel kinematics is carried out.

Human-robot cooperative control system based on serial elastic actuator bowden cable drive in ExoArm 7-DOF upper extremity exoskeleton

The exoskeleton of the upper limb is an external parallel kinematic chain to the human arm. The device is designed to apply a specific torque of interaction to the human body resulting from bilateral teleoperation or rehabilitation. Its task is to work comfortably with the human arm. This paper presents the structure of the developed device and the control system of its joints. The construction of the joints’ drive system was performed based on the Bowden cable transmission. Based on the Bowden cable flexibility, it is possible to control the generated drive torque following the serial elastic actuator concept. The article presents joint control methods minimizing the influence of friction in the closed-loop Bowden cable conduit system. We also present the methods of estimating the torque of interaction with the operator based on the ExoArm 7-DOF exoskeleton dynamics model.

Inverse and forward kinematics and workspace analysis of a novel 5-DOF (3T2R) parallel–serial (hybrid) manipulator

The proposed study provides a solution of the inverse and forward kinematic problems and workspace analysis for a five-degree-of-freedom parallel–serial manipulator, in which the parallel kinematic chain is made in the form of a tripod and the serial kinematic chain is made in the form of two carriages displaced in perpendicular directions. The proposed manipulator allows to realize five independent movements—three translations and two rotations motion pattern (3T2R). Analytical relationships between the coordinates of the end-effector and five controlled movements provided by manipulator’s drives (generalized coordinates) were determined. The approach of reachable workspace calculation was defined with respect to available design constraints of the manipulator based on the obtained algorithms of the inverse and forward kinematics. Case studies are considered based on the obtained algorithms of inverse and forward kinematics. For the inverse kinematic problem, the solution is obtained in accordance with the given laws of position and orientation change of the end-effector, corresponding to the motion along a spiral-helical trajectory. For the forward kinematic problem, various assemblies of the manipulator are obtained at the same given values of the generalized coordinates. An example of reachable workspace designing finalizes the proposed study. Dimensions and extreme values of the end-effector orientation angles are calculated.

Dynamic analysis of a hybrid compliant mechanism with flexible central chain and cantilever beam

Membrane peeling in retinal and cataractous surgery is a challenging task due to physiological hand tremors and delicate tissue. To relieve this problem, we proposed a hybrid compliant mechanism with a flexible central chain and a cantilever beam to suppress hand tremors and vibrate along peeling direction since the vibration can reduce peeling force. The particularly designed mass block makes the axial deformation of central chain and cantilever beam negligible in dynamic modeling. We then studied the dynamic response of the proposed hybrid compliant mechanism. The pseudo-rigid-body model (PRBM) of compliant links, central chain and cantilever beam is given. The relationship between the moving platform and parallel kinematic chains is derived. Next, the full dynamic model is established using the Lagrange equation. Furthermore, the dimension of the full dynamic model is reduced by the proper orthogonal decomposition (POD) method. Simulation results show that the reduced-order model is about 9.0 times faster than the full dynamic model. Experimental results show that the average relative errors of the full dynamic model and the reduced-order model are 2.12% and 1.93%, respectively.

Design of a 3-RPR Flexure System for Optical Switch Assembly

In the MEMS optical switch assembly, the collision is likely to happen between the optical fiber and the U-groove of the chip due to the uncontrollable assembly errors. However, these errors can hardly be completely eliminated by the active control using high precision sensors and actuators. It will cause the large acting force and part damage, which further leads to the assembly failure. To solve this question, this paper presents a novel low-cost three-degree-of-freedom (three-DOF) passive flexure system to adaptively eliminate the planar assembly errors. The flexure system adopts three parallel kinematic chains with a novel 3-RPR structure and has a compact size with a diameter of 125 mm and thickness of 12 mm. A novel eddy current damper with the structure of Halbach array permanent magnets (PMs) is utilized to suppress the adverse mechanical vibration of the assembly system from the background disturbances. Analytical models are established to analyze the kinematic, static, and dynamic performances of the system in detail. Finally, finite element analysis is adopted to verify the established models for optimum design. The flexure system can generate a large deformation of 1.02 mm along the two translational directions and 0.02° along the rotational direction below the yield state of the material, and it has much higher natural frequencies than 200 Hz. Moreover, the large damping force means that the designed ECD can suppress the system vibration quickly. The above results indicate the excellent characteristics of the assembly system that will be applied into the optical switch assembly.

Párhuzamos kinematikájú billenőasztal elemzése

Examining modern five-axis milling machines, it can be concluded that the structural variants lead to machines with different constructions. The variants are mainly determined by the dimensions of the workpieces that can be manufactured on the machine and the kinematic structure of the machine. Based on the kinematic chain of the machine, a distinction can be made between serial kinematic, parallel kinematic and hybrid kinematic chain variants. On simultaneous five-axis machining, the tool and the workpiece perform linear and orientational movements relative to each other simultaneously. In this paper an analysis of variant of a tilting table with parallel kinematics is presented.

A generic approach for analysis of mechanical assembly

Assembly tolerance analysis is increasingly becoming an innovative method for checking whether specified tolerances satisfy assembly functional requirements. Skin model shapes that employ discrete geometry methods can be addressed efficiently when covering geometric tolerances, especially form defects over the product's lifecycle. The point cloud–based discrete geometry uses the actual surfaces to replace the ideal or substitute surfaces in conventional methods, which brings a significant improvement in analysis accuracy and reliability. However, the level of detail and the ordinal simulations restrict their use to simple assemblies. To overcome the issue of the skin model shape in representing deviation propagation, integration of the Jacobian model is proposed; the resulting skin model shapes-Jacobian model combines easy-to-use tolerance propagation and tolerance representation with accuracy guarantees. Besides, Relative positioning method enables calculation of the small displacement torsors for serial or parallel joints, which makes the proposed method a generic approach applicable to both serial and partial parallel kinematic chains. The obtained torsors in the Jacobian model are then used to calculate the final deviations of the functional requirement. The approach is finally illustrated by a practical example.

Position and orientation characteristics of robot mechanisms based on geometric algebra

The operable representation of robot mechanisms is the key to the computerization of type synthesis of parallel mechanisms (PMs). Geometric algebra, an effective mathematical tool for geometric representation and computation, is introduced to describe the position and orientation characteristics (POC) of robot mechanisms, including serial and parallel mechanisms, in this paper. According to the correspondence between the POC of the joint axis and the motion output characteristics of the moving link, the POC union is defined by the outer product operation for the serial kinematic chain and the POC intersection is defined by the shuffle product operation for the parallel kinematic chain. In this paper, a moving coordinate system independent of the position of a mechanism is established for the expression of the joint axes. The direct symbolic algorithm for the motion output characteristics of robot mechanisms, including union and intersection, is proposed and validated via several case studies of 3R open chain, Sarrus linkage, 3-RCC PM and 3-RPS PM. The analysis procedure shows intuition and explicitness that is suitable for computer-aided derivation of the POC set of a mechanism.

Description of a propulsion unit used in guiding a walking machine by recognizing a three-point bordered path

A reconfigurable propulsion unit based on the Peaucellier-Lipkin mechanism has the ability to describe exact straight or curved paths depending on the selected ratio between the lengths of two of its links. The Peaucellier-Lipkin mechanism with one degree of freedom is transformed into a more sophisticated parallel kinematic chain by including four more degrees of freedom. The resulting propulsion unit is able to adapt its kinematic structure and reach instant centers of rotation, in accordance with the presence of three points that border a geometric path. A laser sensor mounted on the body of the machine detects each point. Once the machine has detected the exact location of the border of the road, it walks along a curve parallel to that border. Although the proposed research describes only one propulsion unit or leg, the methodology can be applied to all the legs of the walking machine. The novel 5-DOF leg is able to reach different centers of rotation, providing either the concave or convex arcs that satisfy the basic principle of displacement of walking machines.

Research on kinematics and singularity of a 3-RRR planar hybrid mechanism

This paper studies the kinematics and singularity of a 3-RRR planar hybrid mechanism, which consists of serial and parallel kinematic chains. The configuration characteristics of the 3-RRR planar hybrid mechanism are analysed. The kinematics of the 3-RRR planar hybrid mechanism is solved by applying chaos particle swarm optimisation. The forward position and the inverse position are formulated. Moreover, three kinds of singularities are analysed. The assembly configurations of forward singularity, inverse singularity are obtained, respectively. The results play an important role in practical application for the 3-RRR hybrid mechanism.

Inverse Kinematics for Upper Limb Compound Movement Estimation in Exoskeleton-Assisted Rehabilitation

Robot-Assisted Rehabilitation (RAR) is relevant for treating patients affected by nervous system injuries (e.g., stroke and spinal cord injury). The accurate estimation of the joint angles of the patient limbs in RAR is critical to assess the patient improvement. The economical prevalent method to estimate the patient posture in Exoskeleton-based RAR is to approximate the limb joint angles with the ones of the Exoskeleton. This approximation is rough since their kinematic structures differ. Motion capture systems (MOCAPs) can improve the estimations, at the expenses of a considerable overload of the therapy setup. Alternatively, the Extended Inverse Kinematics Posture Estimation (EIKPE) computational method models the limb and Exoskeleton as differing parallel kinematic chains. EIKPE has been tested with single DOF movements of the wrist and elbow joints. This paper presents the assessment of EIKPE with elbow-shoulder compound movements (i.e., object prehension). Ground-truth for estimation assessment is obtained from an optical MOCAP (not intended for the treatment stage). The assessment shows EIKPE rendering a good numerical approximation of the actual posture during the compound movement execution, especially for the shoulder joint angles. This work opens the horizon for clinical studies with patient groups, Exoskeleton models, and movements types.

A constrained generalised- $$\alpha $$ α method for coupling rigid parallel chain kinematics and elastic bodies

A problem arises from combining flexible rotorcraft blades with stiffer mechanical links, which form a parallel kinematic chain. This paper introduces a method for solving index-3 differential algebraic equations for coupled stiff and elastic body systems with closed-loop kinematics. Rigid body dynamics and elastic body mechanics are independently described according to convenient mathematical measures. Holonomic constraint equations couple both the parallel chain kinematics and describe the coupling between the rigid and continuum bodies. Lagrange multipliers enforce the kinetic conditions for both sets of constraints. Additionally, to prevent numerical inaccuracy from inverting stiff mechanical matrices, a scaling factor normalises the dynamic tangential stiffness matrix. Finally, example tests show the verification of the algorithm with respect to existing computational tests and the accuracy of the model for cases relevant to the problem definition.

Assessment of lower limbs kinematics during human–robot interaction using inertial measurement units

Introduction: The kinematic structure of wearable robots designed for lower limb rehabilitation usually replicates that of the human body (anthropomorphism), thus kinematic incompatibilities may arise from the mismatch between robotic and human joint axes of rotation. Conversely, non-anthropomorphic structures can be designed to be robust against misalignments, thus minimizing undesired interaction forces [1]. A non-anthropomorphic treadmill-based robot for hip and knee flexion/extension assistance, using compliant actuators [2] and deriving human joint kinematic patterns with forward kinematics, has been previously presented [3] and [4]. Inaccuracies in the mapping of rotations from the robot joint space to the human joint space may arise from: (1) human segments length estimation errors, which affect the human–robot parallel kinematic chain, (2) non-rigid human–robot connections and (3) uncertainty associated to the position of fastening points. The aim of this work is to validate the human joints kinematics estimated by the robot (RK) using that provided by inertial measurement units (IK) as reference. Methods:Ahealthy subject (male, 28 y.o.) walked on a treadmill at 0.55, 0.7 and 0.85 m/s wearing the robot. Four inertial measurement units (IMUs – Xsens, MTX, sampling frequency 50 Hz) were attached to the pelvis, thigh, and shank cuffs and to the foot on the right side (Fig. 1). The RK of hip and knee were estimated from the encoders measurements (sampling frequency 200 Hz) using the third-order polynomial approximation of the forward kinematic function derived in [3]. At the beginning of each trial, while the subject was standing (reference configuration), thigh and shank IMUs were mathematically aligned to the pelvis IMU. Hip and knee IK were estimated in terms of sagittal components of the relevant orientation vectors provided by the IMUs. Gait cycles were identified using the acceleration peaks at heel strike. Data from the encoders and IMUs were synchronized using an external trigger. The root mean square deviation (RMSD) between hip and knee RK and IK was computed for the three trials over 10 gait cycles. Results: Representative patterns of hip and knee angles in the sagittal plane (treadmill velocity: 0.55 m/s) are reported. RMSD values averaged over the three different gait speeds were 2.9±0.2◦ for the hip and 4.9±1.2◦ for the knee (mean±sd). In all the trials, maximum discrepancies were found at the peak values (RK peak extension angles were overestimated). Discussion: Non-anthropomorphic robots can offer several advantages in terms of wearability but they may introduce some inaccuracies in the estimation of human joints kinematics. However, results showed that hip and knee RK errors were within levels acceptable in the majority of clinical applications. Moreover, the systematic errors observed can be corrected through a proper calibration of the robot-to-human mapping. The estimate of lower limb kinematics from IMUs integrated in the robotic cuffs could facilitate the control of the robot.

Synthesis of Two-Degree-of-Freedom Rotational Decoupled Manipulators of a 2R-Type Branch

Strong coupling is one of the prominent features of the general parallel mechanisms(Par. Mec.), which has led to difficulty in the trajectory planning and precision control. To solve this problem, the designing of motion decoupled parallel mechanisms(Dec. Par. Mec.) has become a hot topic. This paper, based on the work achieved in our pre-papers, is to make an improvement on the criterion for a branch type synthesis of the rotational decoupled parallel mechanisms(Rot. Dec. Par. Mec.), which ensures the decoupling of the rotations in each limb. This paper focuses on a type synthesis of the decoupled parallel mechanisms with two degree of freedoms (DOFs). Decoupled parallel manipulators with two parallel kinematic chains, one of which is of type 2R(R represents rotation), are taken into consideration in this paper. A large number of novel decoupled architectures are already obtained, some of which have got an application for a China Patent. What has been done in this paper is carried out by means of the screw theory, which has effectively avoided complex equations by synthesis.

Six-axis position measurement system for levitated motion stages

Conventional multi-axis motion measurements are achieved by using single-axis position sensors through serial or parallel kinematic chains, and therefore are susceptible to bearing error motion and structural deformation caused by thermal and mechanical loads. This paper presents a stereo camera-based position measurement system that can directly measure the relative position between two rigid bodies in 6 degrees-of-freedom. Experiments on a magnetically levitated motion stage have demonstrated sub-micron resolution, 16μm uncertainty, and 8000Hz sampling rate in a measurement volume of 400mm×400mm×15mm.

Computed torque control of an under-actuated service robot platform modeled by natural coordinates

The paper investigates the motion planning of a suspended service robot platform equipped with ducted fan actuators. The platform consists of an RRT robot and a cable suspended swinging actuator that form a subsequent parallel kinematic chain and it is equipped with ducted fan actuators. In spite of the complementary ducted fan actuators, the system is under-actuated. The method of computed torques is applied to control the motion of the robot. The under-actuated systems have less control inputs than degrees of freedom. We assume that the investigated under-actuated system has desired outputs of the same number as inputs. In spite of the fact that the inverse dynamical calculation leads to the solution of a system of differential–algebraic equations (DAE), the desired control inputs can be determined uniquely by the method of computed torques. We use natural (Cartesian) coordinates to describe the configuration of the robot, while a set of algebraic equations represents the geometric constraints. In this modeling approach the mathematical model of the dynamical system itself is also a DAE. The paper discusses the inverse dynamics problem of the complex hybrid robotic system. The results include the desired actuator forces as well as the nominal coordinates corresponding to the desired motion of the carried payload. The method of computed torque control with a PD controller is applied to under-actuated systems described by natural coordinates, while the inverse dynamics is solved via the backward Euler discretization of the DAE system for which a general formalism is proposed. The results are compared with the closed form results obtained by simplified models of the system. Numerical simulation and experiments demonstrate the applicability of the presented concepts.

Dynamic Model of a 3-dof Asymmetric Parallel Mechanism

Most research papers about parallel kinematic chain mechanisms investigate symmetric robot manipulators, in which all the limbs connecting the end-effector to the fixed based are composed by the same sequence of links and joints. Contrarily, in some manipulation tasks the velocity and stiffness requirements are anisotropic. In such cases, the asymmetric parallel kinematic chain mechanisms may offer advantages. This works' main objective is to present the inverse dynamic modeling of a 3-dof asymmetric parallel chain mechanism, conceived as a robot manipulator for pick- and-place operations. The type of kinematic structure of the mechanism constrains the motion of the end-effector to only three translations. First, a brief kinematic modeling is carried out. Then, the inverse dynamic modeling is developed by employing the virtual work principle, considering two assumptions: lumped and distributed masses. Based on the model equations, a motion simulation is performed. The same motion is also analyzed by using the ADAMS computing environment to validate the model equations. After the simulation, the results demonstrated a very good agreement between the analyzed variables provided by the dynamic model and those generated by ADAMS. One can also notice that the input torques calculated by the lumped-mass model are quite close to the torques evaluated by the distributed mass model, and might be sufficient for the future development of a motion control law for the mechanism.

Design of decoupled parallel manipulators by means of the theory of screws

Abstract This paper focuses on a study of the decoupling of parallel manipulators. Decoupled parallel manipulators with three parallel kinematic chains are considered. The translation kinematic pairs are designed as planar four-bar parallelograms. The synthesis of these mechanisms is carried out by means of screw groups. This approach allows avoiding completed equations by synthesis and singularity analysis of these mechanisms.

A New Assessment of Singularities of Parallel Kinematic Chains

This paper presents a novel assessment of singularities of general parallel kinematic chains. Hierarchical levels in which different critical phenomena originate are recognized. At each level, the causes of singular events are identified and interpreted, and on their basis, a comprehensive taxonomy is proposed. First, the unactuated kinematic chain is studied. The concepts of leg and passive-constraint singularities are described, and stationary and increased instantaneous mobility configurations are identified. Then, a set of motorized joints is chosen. The effects of first-level singularities on the actuated chain are investigated, and further phenomena are identified, such as redundancy singularities and active-constraint singularities. The notions of reaction and action spaces are originally discussed. The consequences on the ability of the actuated chain to effectively govern its local and global freedoms are analyzed, and the complex interactions between the various singular events are studied. The instantaneous redundancy of actuators, which occur when these work either against each other or against joint constraints, is also evaluated. Finally, when the input-output mechanism is considered, the events described at the previous stages are interpreted within the perspective of the machine's desired use.