Degrees Of Freedom Parallel Manipulator Research Articles

Analysis of coupling effects on hydraulic controlled 6 degrees of freedom parallel manipulator

Analysis of coupling effects on hydraulic controlled 6 degrees of freedom parallel manipulator

Analysis of coupling effects on hydraulic controlled 6 degrees of freedom parallel manipulator

This paper presents an analysis of the coupling effects between degrees of freedom of a hydraulic controlled six DOF parallel manipulator. Based on the singular value decomposition to the properties of its joint space inverse mass matrix, the method is put forward to analyze coupling effects between degrees of freedom using a transformation matrix, the product of transposed Jabobian matrix and an orthogonal unitary matrix, of which each element represents decoupled modal space coordinates with respect to physical task space frame. The simulation results in frequency domain prove the theoretical analysis right. The analysis will provide useful information to mechanism and controller designer, to asses from concept the coupling effects between DOF in respect of the requirement for a particular application and also for the study on decoupling control strategies.

Acausal Approach to Motion Cueing

Motion simulators have been used extensively by both industry and academia to train pilots, conduct psychological experiments on drivers, understand the perception of motion by humans, and cater to the burgeoning gaming industry among others. Working of a motion simulator can be summarized in following three steps: first, acquisition of motion signals; second, motion cueing: signal processing to generate motion references, and third, control: tracking the desired references. A motion cueing algorithm (MCA) acts as a bridge between the actual motions and the ones recreated by the simulator. Mathematically, MCA is constituted of the following four operations: scaling, saturation, filtering, and tilt-coordination (involves filtering too). The existing MCAs make use of causal filters to process the signals, thereby precluding the possibility of utilizing future motion signals to emulate pre-recorded scenarios. We present a new approach to generate motion cues by explicitly making use of future motion signals and causal linear filters. It is due to the usage of future motion signals (not the filter), we call the presented methodology as acausal cueing algorithm (ACA). Unlike most of the existing works on motion cueing, we choose to present the developed methodology using discrete-time models to facilitate its quick implementation by industry and other researchers in the future. The veracity of the presented methodology is examined by actuating a motion simulator (seven degrees of freedom parallel manipulator) based on the references generated by the ACA in response to test trajectories. The conducted experiments assert better performance of the ACA (over MCA) in the beginning, which eventually degrades in the last few seconds due to unavailability of future motion signals.

Spatial Three Degree of Freedom Parallel Manipulator Forward Kinematic Position Analysis

This work presents forward kinematic position analysis of a spatial three degree of freedom parallel manipulator, which has three symmetric loops. The three loops consist of an actuated sliding links- rotational and spherical joints. The actuated sliding links are attached to inclined base platform via rotational joints. The limbs are connected from rotational joints to moving platform by spherical joints. The degree of freedom of a spatial parallel manipulator is analyzed via kutzbach criterion. The forward kinematic position analysis carried out by using 3-coupled trigonometric equations which are formulated with side and behaviour constraints of the manipulator. There are many difficulties in solving the system of non-linear equations in kinematics of manipulator therefore by using MATLAB the three non-linear coupled algebraic equations are solved. The forward position kinematic analysis part is used in the development procedure of spatial parallel manipulator to check, the required and obtained positions of the moving platform of the developed manipulator.

Simultaneous path placement and trajectory planning optimization for a redundant coordinated robotic workcell

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.

Workspace Limiting Strategy for 6 DOF Force Controlled PKMs Manipulating High Inertia Objects

This article describes an efficient and effective strategy for limiting the workspace of a six degrees of freedom parallel manipulator, with challenging motion smoothness requirements due to both the high inertia objects carried by the end effector and the pose references coming from a force feedback loop. Firstly, a suitable formulation of the workspace is studied, distinguishing between different conventions and procedures. Thereafter a discrete and analytical formulation of the workspace is obtained and developed in order to suit this application. Having obtained the limits, a methodology to evaluate the robot pose is discussed, taking into account the reference pose buffering technique and the real time pose estimation through the numeric solution of the nonlinear forward kinematics equations. The safety algorithm designed checks the actual robot pose and future poses to be commanded, and takes control of the reference pose generation process, if an exit of the safety workspace is detected. The result obtained is a soft compliant surface within which the robot is free to move, but outside of which a “force field” pushes the robot end-effector to return smoothly. To reach this objective, the control deflects the end effector trajectory safely and smoothly and moves it back to within the workspace limits. Nevertheless, this preserves the continuity of the velocity and controls the acceleration, to avoid dangerous vibrations and shocks. Simulation and experimental result tests are conducted to verify the algorithm effectiveness and the efficient implementation.

PID Control and Stability Analysis of an ith leg of a Six Degree of Freedom Machining Bed

Process of material removal from work piece to get desired shape is usually termed as machining. Operations such as milling, drilling and turning are categorized as machining. Current spindle techniques allow quick material removal. Performance envelope is limited in such case for higher spindles. The high speed tools are also vulnerable to external and internal vibrations. Cuts made and parts created in existence of these vibrations will result in dimensional inaccuracy and imprecise measurements. A solution of these problems is to restrict the tool motion in a single dimension and instead give Six-DOF to the machine bed. A six degree of freedom robotic mechanism is proposed to tackle this problem to be used as a bed for machining. Proposed machining bed is a six degree of freedom parallel manipulator known as Stewart Platform, in which the tool is fixed and work piece is mounted on a movable top plate which gives controlled motion in six degrees of freedom. Overview of design for a six degree of freedom machining bed is discussed in this paper. The analysis of machining bed is done on MATLAB®. Close loop response, stability through Bode Plot, Nyquist Plot and Root Loci and selection of a controller when working in open loop conditions is discussed in detail in this paper. The results verify that a six degree of freedom bed can be used for the purpose of machining.

Studies on Stewart platform manipulator: A review

This paper presents a compilation of previous studies on the Stewart platform, which is a class of six degree of freedom parallel manipulators. The abstraction of a parallel manipulator is appropriated for the entire class of it. The paper focuses on the studies in the different fields which are closely checked to determine the direction of research and identify the solved problem areas. A significant investigation has been presented to discuss the existing methods for the analysis of the Stewart platform manipulator due to their unique applications. Studies on analysis and design of the Stewart platform manipulator using flexible joints are included. Modeling and analysis of parallel manipulators by Matlab SimMechanics environment are also highlighted.

Mechatronic design, experimental setup, and control architecture design of a novel 4 DoF parallel manipulator

ABSTRACTAlthough parallel manipulators started with the introduction of architectures with six degrees of freedom, a vast number of applications require less than six degrees of freedom. Consequently, scholars have proposed architectures with three and four degrees of freedom, but relatively few four degrees of freedom parallel manipulators have become prototypes, especially of the two rotation and two translation motion types. In this article, we explain the mechatronics design, prototype, and control architecture design of a four degrees of freedom parallel manipulators with two rotation and two translation motions. We chose to design a four degrees of freedom manipulator based on the motion needed to complete the tasks of lower limb rehabilitation. To the author’s best knowledge, parallel manipulators between three and six degrees of freedom for rehabilitation of lower limb have not been proposed to date. The developed architecture enhances the three minimum degrees of freedom required by adding a four degrees of freedom, which allows combinations of normal or tangential efforts in the joints, or torque acting on the knee. We put forward the inverse and forward displacement equations, describe the prototype, perform the experimental setup, and develop the hardware and control architecture. The tracking accuracy experiments from the proposed controller show that the manipulator can accomplish the required application.

Development of a 2-dof uterine manipulator with LED illumination system as a new transvaginal uterus amputation device for gynecological surgeries

Background: Hysterectomy, the most common major gynecological operation worldwide, consists of removal of the uterus and can be performed abdominally, vaginally, or laparoscopically. A uterine manipulator is a key device used for uterine manipulation and cannulation in hysterectomies. The challenges of conventional manipulators are to move the uterus in two distinct planes and to identify cervical landmarks during circular cut and coagulation.Material and methods: In this study, a structural synthesis of the two degrees of freedom parallel manipulator was performed considering the constraints noted by surgeons. Computer-aided design and assembly of the manipulator, the cervicovaginal cap with LEDs, and the external parts were performed before rapid prototyping. The final design of the uterine manipulator was then manufactured from stainless steel and tested on an artificial uterus model using a test chamber.Results: This article presents the design, production and testing processes of an innovative manipulator with a motion capability up to 80° workspace both in the sagittal and coronal planes and an illumination system, easily detectable by the laparoscope, was successfully implemented on the manipulator’s cervical cap in order to overcome the drawbacks of conventional uterine manipulators.Conclusions: Despite all the current studies and uterine manipulators on the market, no research has incorporated all the features mentioned above.

Optimal selection of the supporting points of large component aligned and positioned by parallel manipulator

Large components such as wing sections should be aligned and positioned in a desired position prior to the final manufacturing or assembly, so a digital alignment and position device based on six degree of freedom parallel manipulator with several prismatic-prismatic-prismatic-spherical branches was designed and fabricated to meet the needs. The digital alignment and position device is an alignment device based on the parallel manipulator, and it is also a positioning and holding fixture for large components manufacturing or assembly. In order to effectively and efficiently select the supporting points of large component where the digital alignment and position device branch is connected with, the performance of the parallel manipulator and the fixture should be comprehensively analyzed at the same time. The global performance indices such as the dexterity index, the bearing capacity index, and the stiffness index are calculated based on the mechanism Jacobean matrix of the parallel manipulator, and the positioning stability index is calculated based on the position Jacobean matrix of the fixture. The results show that the global performance indices are not related to the pose, but the positioning stability index is; in addition, all indices rely on the originally selected supporting points and provide the basis for the effective selection of the supporting points for large component aligned and positioned by the digital alignment and position device, which is based on parallel manipulator with prismatic- prismatic-prismatic-spherical pairs.

A novel six degrees-of-freedom parallel manipulator for aircraft fuselage assemble and its trajectory planning

Parallel manipulators have been successfully used for pose adjustment. However, aircraft fuselages are heavy and have complex shapes, so the existing parallel manipulators are not suitable for aircraft fuselages. For the first time, this paper presents a novel six degrees of freedom parallel manipulator for aircraft fuselages. Compared with other parallel manipulators, the presented parallel manipulator is suitable for large round parts. The Jacobi matrix of the presented parallel manipulator is derived, which is expressed by roll, pitch, and yaw. Using the derived Jacobi matrix, inverse kinematics of the presented parallel manipulator is investigated systemically. Combining Newton’s second law with Euler equations, dynamic equations of the manipulator are derived. Using the derived dynamic equations, inverse dynamics of the manipulator are also investigated systemically. For improving safety and efficiency of fuselage pose adjustment, a new trajectory planning algorithm is proposed which is based on the minimum mean force. Simulation experiment results demonstrated the ability of the trajectory planning algorithm to achieve stable movement comparable to the time-optimal trajectory planning algorithm. At the conclusion of this paper, practical applications of the presented parallel manipulator are shown.

Inverse kinematics and rigid-body dynamics for a three rotational degrees of freedom parallel manipulator

Modeling and analysis of inverse kinematics and rigid-body dynamics for a three rotational degrees of freedom (DOF) parallel manipulator are conducted in this research. In the inverse kinematics model, the position, velocity, acceleration, jerk and singularity are considered. The rigid-body dynamic model is developed based on the principle of virtual work and the concept of link Jacobian matrices. In this research, the inverse dynamic analysis of the parallel manipulator is carried out in an exhaustive decoupled way. The total actuating torques, the torques related to the acceleration, velocity, and gravity, the torques related to the moving platform, strut, slider, lead screw, and motor rotor-coupler, and the torques related to external forces are calculated. The total actuating powers, the powers related to the acceleration component of torque, velocity component of torque, gravity component of torque, and the powers related to the moving platform, strut, slider, lead screw, and motor rotor-coupler are also achieved. For the pre-defined trajectory, the required output work for the i-th driving motor is obtained through numerical integration technique. Simulation is conducted to obtain the positions, velocities, accelerations, jerks, torques, powers, and energy consumptions. Jerk computation, singularity formulation and analysis.Rigid-body dynamic model formulation.Inverse dynamic analysis in the decoupled way.Torque, power, and energy consumption computations.The torque and power related to the moving platform are small.

The 3-RPS parallel manipulator from an algebraic viewpoint

The 3-RPS parallel manipulator is a three degree of freedom parallel manipulator, which was introduced by K. Hunt in 1983 as one of the lower mobility parallel manipulators. Since then the 3-RPS gained a lot of attention in literature, but most of the articles on this manipulator use screw theory to explain its local kinematic behavior. An algebraic approach via Study's kinematic mapping reveals interesting global properties of this type of manipulator. The global kinematic behavior of the manipulator is described by algebraic equations, so called constraint equations. In the kinematic analysis these equations are manipulated using methods of algebraic geometry and are interpreted geometrically. It is shown, that the forward kinematics of the 3-RPS has in general 16 solutions in the field of complex numbers. Its workspace splits into two, essentially different operation modes. A geometric and kinematic interpretation of both modes is given. Furthermore it is shown that a transition between the operation modes is possible under certain circumstances. The operation modes are detected via a primary decomposition of the ideal corresponding to the constraint equations. Conditions for singular poses are derived from the constraint equations by discussing the Jacobian of the set of constraint equations. Finally, for singular poses of each operation mode as well as for singular poses belonging to both operation modes, a mapping into the space of joint parameters will be described. Images of singular poses of the manipulator under the mapping determine algebraic surfaces in the joint space, which are analyzed algebraically.

Experimental Investigation on Position Analysis of 3 – DOF Parallel Manipulators

Parallel manipulators (PMs) have been the subject of study, of much robotic research during the past three decades. A parallel manipulator (PM) is a closed loop kinematic chain mechanism, that is connected to the base via multiple independent chains. The scope of this research work is to perform the position analyses of the three degrees of freedom PMs (TRIPOD and TRI-GLIDE). The present work has been planned to model the parallel manipulators using the screw joints for very accurate positioning. Experiments were conducted for the position analysis and the angular tilt of the mobile platform along x-axis and y-axis and they were found by actuating the links of the manipulators. In order to confirm the results obtained by the experimental method, ADAMS was used for solving the kinematic problems involved. The Tri-Glide and Tripod manipulators were created in ADAMS based on the fabricated models. The models were simulated for the displacement of the nut and the angle of tilt / rotation of the mobile platform about the x and y axes. The results obtained by the three methods are discussed and analyzed. In a conventional drilling machine, drilling an angular hole requires special fixtures for each specific angle. In the present work, the parallel manipulator mechanisms have been modified to an angular drilling machine, for performing angular drilling operations.

Convex hull-based velocity transmission capability of parallel manipulators

This paper presents a convex hull-based velocity transmission capability analysis of parallel manipulators (PMs) for more accurate design and performance evaluation of PMs. The velocity transmission capability analysis based on the manipulability ellipsoid does not provide accurate information on how fast a PM can move along an arbitrary direction since the joint velocities are normalized by the two-norm (≤ 1). Therefore, for an accurate velocity transmission capability, a computationally efficient convex hull-based approach is proposed here using minimum infinity-norm solutions. Due to the calculation complexity and the dimensional inconsistency, the velocity transmission capability was analyzed separately for the translational and rotational velocity convex hulls. Moreover, for quantitative measures of the translational and rotational velocities, three performance indices (PI), i.e., local, global, and weighted PI, are proposed to visualize dexterousness of PMs. The proposed method is applied to a general 6 degrees of freedom PM to show the effectiveness of the proposed approach.

SINGULARITY ANALYSIS OF THE 4 RUU PARALLEL MANIPULATOR USING GRASSMANN-CAYLEY ALGEBRA

This paper deals with the singularity analysis of four degrees of freedom parallel manipulators with identical limb structures performing Schönflies motions, namely, three independent translations and one rotation about an axis of fixed direction. The 6 × 6 Jacobian matrix of such manipulators contains two lines at infinity among its six Plücker vectors. Some points at infinity are thus introduced to formulate the superbracket of Grassmann-Cayley algebra, which corresponds to the determinant of the Jacobian matrix. By exploring this superbracket, all the singularity conditions of such manipulators can be enumerated. The study is illustrated through the singularity analysis of the 4-RUU parallel manipulator.

Kinematic and Singularity Analysis of 3 PRR Parallel Manipulator

Three degrees of freedom (DOF) parallel manipulator is used in the applications such as base for various machining operations, drilling inclined holes, airplane and automobile simulators, walking machines, pointing devices, contour milling and machining etc. The 3 DOF parallel manipulator consists of a fixed platform and a movable platform, which are connected by means of three identical links. Pin joints are used to connect the one end of the link and the lead screw pair. This 3 DOF 1R2T parallel manipulator is having one orientation freedom and two translational freedom, which is actuated by means of screw pair, which in turn operated by a stepper motor. The inverse kinematics and velocity equations of this mechanism have been derived mathematically. Based on this inverse kinematics and velocity equations singularity analysis is completed. Two kinds of singularities are compared with ADAMS simulation results and a prototype of the manipulator is developed for further study.

Design of Computer Simulation Model for the Analysis 0f Coupling Effects between Actuators of Hydraulically Driven 6 DOF Parallel Manipulators

This paper presents a computer simulation model to analyze coupling effects between actuators of a hydraulically driven six degrees of freedom parallel manipulators. The design is based on the multi-body dynamics model of the system built using Kane’s formulation and hydromechanics’ principles. Combining the two parts, an integrated computer simulation model is designed to analyze coupling effects using joint space inverse mass matrix. The designed computer simulation model was used to establish a coupling effects relationship between actuators. The simulation results in frequency domain show that the coupling effect is heavier between odd and even numbered actuators. The result further reveal that the dynamics coupling property of the system increase with the frequency and reach the maximum value at the natural frequency. At a frequency higher than the natural frequency the coupling property decreases. This study can assist to provide optimum methods for mechanism designers and can offer a basis for comparing and selection of design options. It can also lay a good foundation for studies on decoupling control strategies.

Dynamic Modeling of a Three Degrees of Freedom Parallel Manipulator for Motion Simulation of Unmanned Vehicle

During the semi-physical simulation experiment of unmanned vehicle,taking into account the features of high precision requirement to motion simulation system,a modified three degrees of freedom parallel manipulator based on the 3-RPS parallel manipulator is proposed.In comparison with the 3-RPS parallel manipulator,because the forces along the spinning shafts of the actuators in 3-RPS parallel manipulator are undertaken by the passive constraints of the modified parallel manipulator,the mechanical properties of the actuators are improved.The kinematic equations are established according to the structure of this parallel manipulator.The dynamic equations of the moving platform are formulated based on the Newton-Euler method.In the light of the principle of moment equilibrium,a force which is perpendicular to the actuator and its spinning shaft is worked out,and a force which is perpendicular to the upper part of the passive constraint and its spinning shaft is also worked out.According to the principle of power balance,a force along the upper part of the passive constraint is calculated.The driving forces of the actuators and the forces along the spinning shafts of the passive constraints can be obtained finally.This calculation method sheds light on dynamics calculation of lower mobility parallel manipulators.