3-DOF Parallel Mechanism Research Articles

An experimental dynamic identification & control of an overconstrained 3-DOF parallel mechanism in presence of variable friction and feedback delay

The closed-loop dynamic control of parallel mechanisms is a challenging field due to the high complexity of their dynamic behavior, especially those with prismatic actuators. Prismatic joints usually provide considerable amount of friction which could vary along its axis. This paper addresses the application of different control algorithms in order to tackle the challenges in closed-loop control of an overconstrained 3-DOF decoupled parallel mechanism which compromises three prismatic actuators with variable frictions along each axis. In addition, a Kinect vision sensor, as the position feedback, is installed. Since the Kinect RGB sensor performs at 30 frame per second, there is a 33 ms delay in the feedback of the control unit which restricts the control loop frequency to maximum value of 30 Hz. Then, based on the models obtained from the identifications of step response, kinetic friction and inverse dynamic model, various attempts have been made in order to obtain a controller with a reasonably performance. First, the conventional PID and sliding mode controllers are applied. Then, the position–velocity controller based on the obtained experience of the mechanism performance is proposed, in which a feedforward unit as the friction compensator is added to the latter feedback-based control units. Eventually, a feedback–feedforward controller based on PID controller and a compensator based on the identified inverse dynamic model is applied to the mechanism which was able to improve the performance of the control unit to a sufficient level.

Type Synthesis of 5-DoF Parallel Mechanisms with Different Submechanisms

The type synthesis of the 5-DoF (degree of freedom) parallel mechanisms with different submechanisms is studied by utilizing digital topology graphs (DTGs). The conditions for synthesizing the 5-DoF parallel mechanisms with different submechanisms using DTGs are determined. Many valid DTGs are derived from 17 different 5-DoF associated linkages, and the valid DTGs are transformed into revised DTGs. The subplanar and/or spatial parallel mechanisms in the 5-DoF parallel mechanisms are transformed into some simple equivalent limbs, and their equivalent relations and merits are analyzed. Using the derived valid DTGs and revised DTGs, many 5-DoF parallel mechanisms with different subserial or parallel mechanisms are synthesized, and they are simplified by replacing the complicated subparallel mechanisms with their simple equivalent limbs. Finally, their DoFs are calculated to verify the correctness and effectiveness of the proposed approach.

Closed-form solutions of the kinetostatics of a 2limbs 6 dof parallel mechanism with kinematic and actuation redundancies

Closed-form solutions of the kinetostatics of a 2limbs 6 dof parallel mechanism with kinematic and actuation redundancies

Kinematic design of a footplate drive mechanism using a 3-DOF parallel mechanism for walking rehabilitation device

Kinematic design of a footplate drive mechanism using a 3-DOF parallel mechanism for walking rehabilitation device

Modeling and controller design of a 6-DOF precision positioning system

Abstract A key hurdle to meet the needs of micro/nano manipulation in some complex cases is the inadequate workspace and flexibility of the operation ends. This paper presents a 6-degree of freedom (DOF) serial-parallel precision positioning system, which consists of two compact type 3-DOF parallel mechanisms. Each parallel mechanism is driven by three piezoelectric actuators (PEAs), guided by three symmetric T-shape hinges and three elliptical flexible hinges, respectively. It can extend workspace and improve flexibility of the operation ends. The proposed system can be assembled easily, which will greatly reduce the assembly errors and improve the positioning accuracy. In addition, the kinematic and dynamic model of the 6-DOF system are established, respectively. Furthermore, in order to reduce the tracking error and improve the positioning accuracy, the Discrete-time Model Predictive Controller (DMPC) is applied as an effective control method. Meanwhile, the effectiveness of the DMCP control method is verified. Finally, the tracking experiment is performed to verify the tracking performances of the 6-DOF stage.

Kinematic calibration of a 3-DOF parallel tool head

PurposeThe purpose of this study is to develop a modified parameter identification method and a novel measurement method to calibrate a 3 degrees-of-freedom (3-DOF) parallel tool head. This parallel tool head is a parallel mechanism module in a five-axes hybrid machine tool. The proposed parameter identification method is named as the Modified Singular Value Decomposition (MSVD) method. It aims to overcome the difficulty of choosing the algorithm parameter in the regularization identification method. The novel measurement method is named as the vector projection (VP) method which is developed to expand the measurement range of self-made measurement implements.Design/methodology/approachNewton Iterative Algorithm based on Least Square Method is analyzed by using the Singular Value Decomposition method. Based on the analysis result, the MSVD method is proposed. The VP method transforms the angle measurement into the displacement measurement by taking full advantage of the ability that the 3-DOF parallel tool head can move in the X – Y plane.FindingsThe kinematic calibration approach is verified by calibration simulations, a Rotation Tool Center Point accuracy test and an experiment of machining an “S”-shaped test specimen.Originality/valueThe kinematic calibration approach with the MSVD method and VP method could be successfully applied to the 3-DOF parallel tool head and other 3-DOF parallel mechanisms.

Review on 2R1T 3-DOF parallel mechanisms

Mechanisms are the skeletons and end-effectors of manufacturing equipments. The innovation of mechanism is indispensable to the independent innovation of manufacturing equipments. Compared with serial industrial manipulators, parallel mechanisms offer high rigidity, good dynamic response, potential high accuracy and large payload capability with the price of less dexterity, complex distribution of singular configurations and limited workspace. Over the last two decades, lower-mobility parallel mechanisms whose degrees of freedom (DOF) are fewer than six have been successfully implemented in many applications like positioning, orientation, and axis-symmetrical machining, which do not reqiure all six DOFs. With the well optimized architecture of a lower-mobility parallel mechanism, the reduced cost of fabrication, actuation, control and maintenance can be obtained compared with their 6-DOF counterparts. The 2R1T (R: rotation, T: translation) 3-DOF parallel mechanisms are most typical examples of successful applications in advanced manufacturing equipments such as parallel kinematic machine, industrial robot, and articulated tool head. Based on the relative geometrical relations between the two axes of rotation, the 2R1T 3-DOF parallel mechanism is classified into four categories: UP, PU, RPR and P*U*. The motion of the moving platform of a UP (U: universal joint, P: prismatic joint) parallel mechanism can be generated by a UP serial chain, including a rotation about a fixed axis, a rotation about a moving axis perpendicular to the fixed one, and a translation along the normal of the two axes. The motion of the moving platform of a PU parallel mechanism can be generated by a PU serial chain, including a rotation about an orientation-fixed axis, a rotation about a moving axis perpendicular to the orientation-fixed one, and a translation perpendicular to the orientation-fixed one. The motion of the moving platform of a RPR parallel mechanism can be generated by a RPR serial chain, including a rotation about a fixed axis near the base, a translation perpendicular to the fixed revolute axis and a rotation about a moving axis perpendicular to the orientation-fixed one. When the orientation and position of the two rotational axes of a 2R1T parallel mechanism are time varying, the motion of the moving platform cannot be modeled by a 3-DOF serial chain and is denoted by a virtual serial chain P*U*. The current research status of study on type synthesis, performance analysis and dimensional synthesis of the UP, PU, RPR and P*U* parallel mechanisms are reviewed and discussed. It is worth noting that despite the fact that many well-acknowledged progresses have been obtained by Chinese researchers in type synthesis, kinematic analysis and synthesis of lower-mobility parallel mechanisms, there is still a lack of basic principles and methods for selecting the architectures with engineering potentials from the massive outputs of type synthesis. This is an important challenge that the Chinese researchers in the fundamental research area of parallel mechanisms must face to support the self-innovation of manufacturing equipments. In addition, there are many open problems concerning rigid-flexible coupled dynamic design, accuracy calibration, and control of 2R1T 3-DOF parallel mechanisms, which require an immediate deployment of systematic and thorough research.

Kinematic effects of number of legs in 6-DOF UPS parallel mechanisms

SUMMARYIn this paper, we study the kinematic effects of number of legs in 6-DOF UPS parallel manipulators. A group of 3-, 4-, and 6-legged mechanisms are evaluated in terms of the kinematic performance indices, workspace, singular configurations, and forward kinematic solutions. Results show that the optimum number of legs varies due to priorities in kinematic measures in different applications. The non-symmetric Wide-Open mechanism enjoys the largest workspace, while the well-known Gough–Stewart (3–3) platform retains the highest dexterity. Especially, the redundantly actuated 4-legged mechanism has several important advantages over its non-redundant counterparts and different architectures of Gough–Stewart platform. It has dramatically less singular configurations, a higher manipulability, and at the same time less sensitivity. It is also shown that the forward kinematic problem has 40, 16, and 1 solution(s), respectively for the 6-, 3-, and the 4-legged mechanisms. Superior capabilities of the 4-legged mechanism make it a perfect candidate to be used in more challenging 6-DOF applications in assembly, manufacturing, biomedical, and space technologies.

Structure Characteristics and Kinematic Analysis of Redundant 6-DOF Parallel Mechanism

Structure Characteristics and Kinematic Analysis of Redundant 6-DOF Parallel Mechanism

Design of a biologically inspired lower limb exoskeleton for human gait rehabilitation.

This paper proposes a novel bionic model of the human leg according to the theory of physiology. Based on this model, we present a biologically inspired 3-degree of freedom (DOF) lower limb exoskeleton for human gait rehabilitation, showing that the lower limb exoskeleton is fully compatible with the human knee joint. The exoskeleton has a hybrid serial-parallel kinematic structure consisting of a 1-DOF hip joint module and a 2-DOF knee joint module in the sagittal plane. A planar 2-DOF parallel mechanism is introduced in the design to fully accommodate the motion of the human knee joint, which features not only rotation but also relative sliding. Therefore, the design is consistent with the requirements of bionics. The forward and inverse kinematic analysis is studied and the workspace of the exoskeleton is analyzed. The structural parameters are optimized to obtain a larger workspace. The results using MATLAB-ADAMS co-simulation are shown in this paper to demonstrate the feasibility of our design. A prototype of the exoskeleton is also developed and an experiment performed to verify the kinematic analysis. Compared with existing lower limb exoskeletons, the designed mechanism has a large workspace, while allowing knee joint rotation and small amount of sliding.

A new neural gas network approach for obtaining the singularity-free workspace of 3-DOF planar parallel manipulators

This paper proposes a new extension of the Growing Neural Gas Network, called the Progressive Growing Neural Gas Network (PGNGN), for the application of kinematic investigation of parallel mechanisms, with more emphasis on the singularity-free workspace determination. In fact, PGNGN leads to a general approach in order to obtain the topology of the workspace. In this algorithm, the network starts to grow by taking into account new data points close to its border neurons by resorting to the so-called boundary data generation procedure. By considering singularity loci expression, the separated parts are detected and each part will pursue learning, adding units and connections, until a given performance criterion will be reached. Finally, after finding cavities, if any exists, the maximal circle for each part of the workspace is found. A graphical user interface (GUI) is developed providing the users with easy access to the important parameters in which the singularity-free workspace of three planar three-degree-of-freedom (3-DOF) parallel mechanisms are investigated in which two of them, namely, 3-RRR and 3-PRR parallel mechanisms, are among the most complicated parallel mechanisms due to their highly nonlinear and complicated singularity loci expressions. Results reveal the applicability and reliability of the proposed PGNGN-based approach for obtaining the singularity-free workspace of planar parallel mechanisms.

Design of a 2DOF parallel mechanism to assist therapies for knee rehabilitation

<p>This paper presents a knee rehabilitation device to reproduce four exercises generally used in the rehabilitation therapies. The device consists of a mechanical structure based on a 2 DOF parallel mechanism, a controller with PIC-SERVO motion control boards, and a GUI that commands the device to reproduce the rehabilitation exercises. The position kinematic analysis of the mechanism is developed as well as its dimensioning synthesis to cover various leg sizes. This work proposes a technological alternative with significant advantages that responds to the global need for improving physical knee rehabilitation process. A prototype was manufactured and its mobility was validated using a mannequin.</p>

Solar.q_1: A new solar-tracking mechanism based on four-bar linkages

This paper describes the early stages of the design process of a 2-DOF parallel mechanism, based on the use of four-bar linkages and intended to move photovoltaic panels in order to perform sun tracking. Primary importance is given to the search for a way to compensate sun–earth’s relative motions with two decoupled rotations of the panel. This leads to devise a kinematic structure characterized by a particular arrangement of the revolute axes. At the same time, the structure itself is designed in order to be slender. Subsequently, the fact that during a day the earth’s revolution around the sun has negligible effects on the apparent trajectory of the sun, if compared to the rotation around the polar axis, leads to choose a control strategy which, also thanks to the said arrangement of axes, employs only 1-DOF for most of the daytime. The tracker which employs this strategy has, theoretically, an energy consumption similar to that of 1-DOF solar trackers but a precision similar to that of 2-DOF ones.

Development of synchronized control system through a pneumatic parallel mechanism and its 3D CG model

This study developed a rehabilitation system that can improve the patient care services provided by physical therapists. Wristparalyzed patients were given arbitrary force through a six-Degree of freedom (6DoF) parallel mechanism composed of six pneumatic cylinders, and recovery training was performed. Each pneumatic cylinder was used to apply force control using a pulse width modulation control, and the force of the 6DoF direction was directed to the wrist of the patient. The thrust force of each cylinder and the force of the 6DoF direction of the parallel mechanism were analyzed. The analysis results conformed well to the experimental results. The developed rehabilitation system was designed to help a physical therapist remotely treat multiple patients at the same time. To monitor the operation of the parallel mechanism of each patient’s side, a 3D computer graphic model was created through OpenGL. The movement of this model was investigated to further examine the movement of the 6DoF direction of the parallel mechanism. Results confirmed that both movements can be controlled synchronously.

Singularity-Free Workspace Aimed Optimal Design of a 2T2R Parallel Mechanism for Automated Fiber Placement

This paper introduces a new concept of applying a parallel mechanism in automated fiber placement (AFP) for aerospace part manufacturing. By investigating the system requirements, a 4DOF parallel mechanism consisting of two revolute–prismatic–spherical joints (2RPS) and two universal–prismatic–spherical joints (2UPS) limbs with two rotational (2R) and two translational (2T) motions is proposed. Both inverse and forward kinematics models are obtained and solved analytically. Based on the overall Jacobian matrix in screw theory, singularity loci are presented and the singularity-free workspace is correspondingly illustrated. To maximize the singularity-free workspace, locations of the 2UPS limbs with the platform and base sizes are used in the optimization which gives a new design of a 4DOF parallel mechanism. A dimensionless Jacobian matrix is also defined and its condition number is used for optimizing the kinematics performance in the optimization process. A numerical example is presented with physical constraint considerations of a test bed design for AFP.

Type synthesis of spatial 3-DoF parallel mechanisms with planar sub-chains using revised digital topological graphs and arrays

SUMMARYType synthesis of spatial 3-DoF (degree of freedom) parallel mechanisms (PMs) with planar sub-chains is studied using the revised digital topology graph (r-DTGs) and arrays. First, many DTGs for type synthesis of spatial 3-DoF PMs are derived from their contracted graphs (CGs). Second, a complicated derivation of the DTG and an identification of an isomorphic DTG are transformed into a simple derivation of an array and an identification of an isomorphic array using a compiled program. Third, one or more spatial closed-loop chains in the derived DTGs are changed into the planar closed-loop chains by modifying digits marked in closed-loop chains, and the DTGs are transformed into the r-DTGs for the type synthesis of the spatial 3-DoF PMs with planar sub-chains. Finally, the 52 novel spatial 3-DoF PMs with the planar sub-chains are synthesized and verified by simulation mechanisms.

Rigid Dynamic Model and Analysis of 5-DOF Parallel Mechanism

This paper introduces a novel 4-UPS-RPS spatial parallel mechanism, which can achieve three rotation degrees and two translation degrees of freedom. A rigid dynamic model is established and analysis of the parallel mechanism is carried out. The kinematics of the RPS and UPS driving limbs are analysed and the velocity-mapping relationships between the driving limbs and the other parts are built. The load conditions of the parts are analysed, and the rigid dynamic model of the 4-UPS-RPS parallel mechanism is derived by the virtual work principle approach. Using the example of the parallel mechanism movement, a driving forces analysis of the 4-UPS-RPS parallel mechanism is carried out, and the correctness of the rigid dynamic model is verified by numerical calculation and virtual simulation.

Conceptual design and optimization of a 3-DoF parallel mechanism for a turbine blade grinding machine

This paper firstly presents the conceptual design of a turbine blade grinding machine, and a hybrid mechanism with six degrees of freedom (DoFs) is proposed for the development of the machine. In this concept, a 3-DoF parallel kinematic mechanism is used to realize the high-speed and high dynamic performance. To ensure that the 3-DoF parallel kinematic mechanism has continuous workspace, the singularity is analyzed and discussed in detail. By taking motion/force transmissibility into consideration, kinematic optimization is carried out based on a local transmission index and the geometrical parameters are derived. The conceptual design and optimization presented in this paper are very helpful to the development of the turbine blade grinding machine.

Design of a new 6-DOF parallel mechanism with a suspended platform

This paper deals with the kinematics and analysis of a new parallel mechanism with a suspended platform. The proposed mechanism has a unique appearance in that the 6 chains originating from a circular ring are connected to the both ends of a suspended platform. After introducing the kinematics, the architecture singularity problem is analyzed. Then, the kinematic characteristics of this mechanism are analyzed with respect to the workspace and the isotropic index. Kinematic optimization of this mechanism was also performed. Finally, the proposed robot was employed as an automatic device for otologic surgery.

Performance Analysis of 3-URU Spherical Parallel Mechanism Designed Based on Velocity Transmission and Force Constraint Indices

In this paper was observed performances of developed three degrees of freedom (dof) parallel mechanism named 3-URU spherical parallel mechanism. The mechanism is composed of three identical limbs mounted symmetrically to base (fixed link) and platform (output link). The limb is constructed by universal-revolute and universal joints. The kinematic constants of mechanism consisting of link lengths, radius of platform, radius of base, mounting angle of limb and platform to base and platform were determined with consideration of velocity transmission and force constraint indices. To evaluate performance of mechanism, it was manufactured a prototype of mechanism designed base on these two mentioned indices. There are three steps proposed to realize the mechanism, (i) kinematic synthesis to determine of kinematic constants, (ii) design of mechanical components to define shape and dimension of links and joints by considering collision in wokingspace and static analysis, (iii) evaluation of mechanism performances consisting of workingspace, controllability of platform motion and static payload. Based on obtained results, it can be clarified that, the mechanism can produce spherical motion of platform which rotates on steady point recognized as center of platform rotation. The platform can achieve maximum inclination angle, 80 degree and at this posture occurs translational error, 0.0102 mm. On the other hand, the mechanism can support payload ten times of weight of moving parts.