FORWARD KINEMATICS ANALYSIS FOR A NOVEL 5-DOF PARALLEL MECHANISM USING TETRAHEDRON CONFIGURATIONS

Forward kinematics analysis of a novel 5-DOF parallel mechanism using tetrahedron configurations is presented. Such mechanism is suitable to many tasks requiring less than 6 DOFs. It consists of a movable platform connected to the base by five identical 6-DOF active limbs plus one active limb with its DOF being exactly the same as the specified DOF of the movable platform, which leads to its legs＇ topology 4-UPS/UPU. Based on the tetmhedron geometry, both closed-form solution with an extra sensor and numerical method using iterative algorithm are employed to obtain the forward kinematics solutions of the mechanism. Compared with the conventional methods, the proposed closed-form solution has the advantages in automatically avoiding unnecessary complex roots and getting a unique solution for the forward kinematics. Finally, an example shows that the proposed numerical algorithm is so effective that it enables a real-time forward kinematics solution to be achieved and the initial value can be chosen easily.

Configuration and Kinematics of a 3-DOF Generalized Spherical Parallel Mechanism for Ankle Rehabilitation

The kinematic equivalent model of an existing ankle-rehabilitation robot is inconsistent with the anatomical structure of the human ankle,which influences the rehabilitation effect.Therefore,this study equates the human ankle to the UR model and proposes a novel three degrees of freedom(3-DOF)generalized spherical parallel mechanism for ankle rehabilitation.The parallel mechanism has two spherical centers corresponding to the rotation centers of tibiotalar and subtalar joints.Using screw theory,the mobility of the parallel mechanism,which meets the requirements of the human ankle,is analyzed.The inverse kinematics are presented,and singularities are identified based on the Jacobian matrix.The workspaces of the parallel mechanism are obtained through the search method and compared with the motion range of the human ankle,which shows that the parallel mechanism can meet the motion demand of ankle rehabilitation.Additionally,based on the motion-force transmissibility,the performance atlases are plotted in the parameter optimal design space,and the optimum parameter is obtained according to the demands of practical applications.The results show that the parallel mechanism can meet the motion requirements of ankle rehabilitation and has excellent kinematic performance in its rehabilitation range,which provides a theoretical basis for the prototype design and experimental verification.

Kinematics Analysis and Singularity Avoidance of a Parallel Mechanism with Kinematic Redundancy

The kinematic redundancy is considered as a way to improve the performance of the parallel mechanism.In this paper,the kinematics performance of a three degree-of-freedom parallel mechanism with kinematic redundancy(3-DOF PM-KR)and the influence of redundant parts on the PM-KR are analyzed.Firstly,the kinematics model of the PM-KR is established.The inverse solutions,the Jacobian matrix,and the workspace of the PM-KR are solved.Secondly,the influence of redundancy on the PM-KR is analyzed.Since there exists kinematic redundancy,the PM-KR possesses fault-tolerant performance.By locking one actuating joint or two actuating joints simultaneously,the fault-tolerant workspace is obtained.When the position of the redundant part is changed,the workspace and singularity will be changed.The results show that kinematic redundancy can be used to avoid singularity.Finally,the simulations are performed to prove the theoretical analysis.

DYNAMICS ANALYSIS OF 2-DOF SPHERICAL PARALLEL MECHANISM

The analytical formulations of the velocity and the acceleration of a 2-DOF spherical parallel mechanism are derived by the screw theory. Based on building its dynamics model by the principle of virtual work and reciprocal product of the screw, the equation of the motor moment is obtained. Through the transformation of dynamics model, the configuration space method of the dynamics equation and the corresponding coefficients are presented. Finally, the result of an example shows that the inertia moment and the gravity play a more important role than the coriolis and centrifugal moment, and the former is ten times of the latter in the magnitude. So, the latter can be neglected only when the velocity of mechanism is very slow.

Generalized Kinematics Analysis of Hybrid Mechanisms Based on Screw Theory and Lie Groups Lie Algebras

Advanced mathematical tools are used to conduct research on the kinematics analysis of hybrid mechanisms,and the generalized analysis method and concise kinematics transfer matrix are obtained.In this study,first,according to the kinematics analysis of serial mechanisms,the basic principles of Lie groups and Lie algebras are briefly explained in dealing with the spatial switching and differential operations of screw vectors.Then,based on the standard ideas of Lie operations,the method for kinematics analysis of parallel mechanisms is derived,and Jacobian matrix and Hessian matrix are formulated recursively and in a closed form.Then,according to the mapping relationship between the parallel joints and corresponding equivalent series joints,a forward kinematics analysis method and two inverse kinematics analysis methods of hybrid mechanisms are examined.A case study is performed to verify the calculated matrices wherein a humanoid hybrid robotic arm with a parallel-series-parallel configuration is considered as an example.The results of a simulation experiment indicate that the obtained formulas are exact and the proposed method for kinematics analysis of hybrid mechanisms is practically feasible.

INVERSE KINEMATIC AND DYNAMIC ANALYSIS OF A 3-DOF PARALLEL MECHANISM

According to the structure character of the passive sub-chain of the 3TPS-TPparallel mechanism, the kinematic constraint equations of the movable platform are established,based on which the closed-form inverse kinematics formula of the parallel mechanism are presented.Through parting the spherical joints of the active sub-chains and using the force and momentequilibrium of both the active sub-chains and passive sub-chain, the constraint forces acting on theparted joints are determined. Subsequently, the analytic expressions of the actuator driving forcesare derived by means of the force equilibrium of the upper links of active sub-chains.

PERFORMANCE ANALYSIS AND KINEMATIC DESIGN OF PURE TRANSLATIONAL PARALLEL MECHANISM WITH VERTICAL GUIDE-WAYS

Performance analysis and kinematic design of the 3-PUU pure translational parallel mechanism with vertical guide-ways are investigated. Two novel performance indices, the critical slider stroke and the main section area of workspace, are defined; The expressions of two other indices, i.e. the global dexterity and global force transfer ratio are revised based on the main section of workspace. Using these indices, performance changes versus the varieties of dimensional parameters of mechanism are investigated in detail and the graphic descriptions of change tendencies of the performance indices are illustrated. By means of these obtained graphic descriptions, kinematic parameters for the 3-PUU pure translational parallel mechanism with better characteristics can be directly acquired.

Analysis and Simulation of Kinematical Performances of Two Kinds of Parallel Mechanisms Based on the Plane Sprayer

Two kinds of 2-dof parallel mechanisms are proposed in this paper which can be used as the actuator for the plane sprayer. The direct and inverse kinematics solutions of the two kinds of mechanisms are derived on the end operating point and two workspaces are analyzed and compared. The kinematics models of the end operating point of two mechanisms are simulated by Matlab examples obtaining variation of kinematics parameters of these two mechanisms. The research of this paper provides the basis for the selection of mechanism, trajectory planning of the end operating point on the sprayer and often some practical value for trajectory analysis and structure design of the plane sprayer.

Kinematic,Workspace and Force Analysis of A Five-DOF Hybrid Manipulator R(2RPR)R/SP+RR

In the present study,the over-constrained hybrid manipulator R(2RPR)R/SP+RR is considered as the research objective.In this paper,kinematics of the hybrid manipulator,including the forward and inverse position,are analyzed.Then,the workspace is checked based on the inverse position solution to evaluate whether the workspace of the hybrid manipulator meets the requirements,and the actual workspace of the hybrid robot is analyzed.After that,the force analysis of the over-constrained parallel mechanism is carried out,and an ADAMS-ANSYS rigid-flexible hybrid body model is established to verify the simulation.Based on the obtained results from the force analysis,the manipulator structure is designed.Then,the structure optimization is carried out to improve the robot stiffness.Finally,calibration and workspace verification experiments are performed on the prototype,cutting experiment of an S-shaped aluminum alloy workpiece is completed,and the experiment verifies the machining ability of the prototype.This work conducts kinematics,workspace,force analyses,structural optimization design and experiments on the over-constrained hybrid manipulator R(2RPR)R/SP+RR,providing design basis and technical support for the development of the novel hybrid manipulator in practical engineering.

The Kinematics Analysis of the Hydraulic Mine-clearing Mechanical Manipulator

Through analyzing the kinematics of the hydraulic manipulator operating system, according to the rules for seting up the D-H coordinate system, the generalized coordinate of the manipulator system is established. The rotating and moving joints are selected from the mechanism as joint variables. Each generalized transformation matrix of joints is worked out. The kinematics equation at the finger end of the manipulator is calculated. The obverse solution for the manipulator is gained. The geometrical operating parameters and primary technical specification of the manipulator system are simulated through the computer. The simulative result has shown that the manipulator operating system meets the working task requirements. This research provides theoretical basis for optimizing structural parameters of the manipulator operating. So it also is justified the feasibility for mechanical manipulators to be used in the engineering equipment platform of the hydraulic excavator.

Error Analysis of Three Degree-of-Freedom Changeable Parallel Measuring Mechanism

A three degree-of-freedom (DOF) planar changeable parallel mechanism is designed by means of control of different drive parameters. This mechanism possesses the characteristics of two kinds of parallel mechanism. Based on its topologic structure, a coordinate system for position analysis is set-up and the forward kinematic solutions are analyzed. It was found that the parallel mechanism is partially decoupled. The relationship between original errors and position-stance error of moving platform is built according to the complete differential-coefficient theory. Then we present a special example with theory values and errors to evaluate the error model, and numerical error solutions are gained. The investigations concentrating on mechanism errors and actuator errors show that the mechanism errors have more influences on the position-stance of the moving platform. It is demonstrated that improving manufacturing and assembly techniques can greatly reduce the moving platform error. The small change in position-stance error in different kinematic positions proves that the error-compensation of software can improve considerably the precision of parallel mechanism.

Design and Analysis of a Novel 2T2R Parallel Mechanism with the Closed-loop Limbs

This paper presents a novel four degrees of freedom(DOF) parallel mechanism with the closed-loop limbs, which includes two translational(2 T) DOF and two rotational(2 R) DOF. By connecting the proposed parallel mechanism with the guide rail in series,the 5-DOF hybrid robot system is obtained, which can be applied for the composite material tape laying in aerospace industry. The analysis in this paper mainly focuses on the parallel module of the hybrid robot system. First, the freedom of the proposed parallel mechanism is calculated based on the screw theory. Then, according to the closed-loop vector equation, the inverse kinematics and Jacobian matrix of the parallel mechanism are carried out. Next, the workspace stiffness and dexterity analysis of the parallel mechanism are investigated based on the constraint equations, static stiffness matrix and Jacobian condition number. Finally, the correctness of the inverse kinematics and the high stiffness of the parallel mechanism are verified by the kinematics and stiffness simulation analysis, which lays a foundation for the automatic composite material tape laying.

Design and analysis of the gripper mechanism based on generalized parallel mechanisms with configurable moving platform

Generalized parallel mechanisms with a configurable moving platform have become popular in the research field of parallel mechanism.This type of gripper mechanism can be applied to grasp large or heavy objects in different environments that are dangerous and complex for humans.This study proposes a family of novel(5+1)degrees of freedom(three translations and two rotations plus an additional grasping motion)gripper mechanisms based on the generalized parallel mechanisms with a configurable moving platform.First,the configurable moving platform,which is a closed loop,is designed for grasping manipulation.The hybrid topological arrangement is determined to improve the stiffness of the manipulator and realize high load-to-weight ratios.A sufficient rule based on Lie group theory is proposed to synthesize the mechanism.TTie hybrid limb structure is also enumerated.A family of novel gripper mechanisms can be assembled through the hybrid limbs by satisfying the rule.Two examples of the gripper mechanisms with and without parallelogram pairs are shown in this study.A kinematic analysis of the example mechanism is presented.The workspace shows that the mechanism possesses high rotational capability.In addition,a stiffiiess analysis is performed.

Kinematic and Dynamic Analysis of a 3-■US Spatial Parallel Manipulator

Parallel Kinematic Machines(PKMs)are being widely used for precise applications to achieve complex motions and variable poses for the end effector tool.PKMs are found in medical,assembly and manufacturing industries where accuracy is necessary.It is often desired to have a compact and simple architecture for the robotic mechanism.In this paper,the kinematic and dynamic analysis of a novel 3-PRUS(P:prismatic joint,R:revolute joint,U:universal joint,S:spherical joint)parallel manipulator with a mobile platform having 6 Degree of Freedom(Do F)is explained.The kinematic equations for the proposed spatial parallel mechanism are formulated using the Modified Denavit-Hartenberg(DH)technique considering both active and passive joints.The kinematic equations are used to derive the Jacobian matrix of the mechanism to identify the singular points within the workspace.A Jacobian based sti ness analysis is done to understand the variations in sti ness for different poses of the mobile platform and further,it is used to decide trajectories for the end effector within the singularity free region.The analytical model of the robot dynamics is presented using the Euler-Lagrangian approach with Lagrangian multipliers to include the system constraints.The gravity and inertial forces of all links are considered in the mathematical model.The analytical results of the dynamic model are compared with ADAMS simulation results for a pre-defined trajectory of the end effector.

Kineto-static analysis of a novel high-speed parallel manipulator with rigid-flexible coupled links

A novel high-speed parallel kinematic machine （PKM） named Delta-S parallel manipulator is proposed, which consists of a fixed base connected to a moving platform through three limbs with identical topology. Each limb is composed of one driving ann and one follower arm, herein, the latter includes two strings and one middle rod, all located in a same plane. Compared with similar manipulators with uniform parameters, the novel and unique topology as well as the addition of two strings of Delta-S manipulator can remove the clearance of the spherical joints, reduce the inertial load of components further, improve the positioning accuracy and dynamic performance, and so on. In order to formulate the kineto-static model of Delta-S manipulator, the kineto-static analyses and models of the driving arm, the generalized follower and the moving platform can be carried out by the D＇ALEMBERT principle. For the sake of obtaining the force analytic results of strings, the deformation compatibility condition of strings and the middle rod are determined. Furthermore, in virtue of the assumption of small deformation and the linear superposition principle, the minimal pre-tightening force of the strings is calculated. The main results include that the loads of the strings and the middle rod must be larger than ＂zero＂ and the pre-tightening force over the workspace must be larger than the minimal pre-tightening force at any time within the workspace, which lay the foundation for the dynamic analysis and the prototype manufacture of the Delta-S manipulator.

Research on Novel Linear Driving and Metamorphic Characteristics for Slider-actuated Parallel (Hybrid) Mechanism

This paper presents a novel one-axis linear-drive control system, in which wire rope is wound orderly around drum by servo motor drive and drays the working slider for a long linear reciprocating motion. PKM with this control system is metamorphic and can achieve great feed forces, accelerations and transverse speeds, high accuracy and low cost. The metamorphic characteristics are studied, including the metamorphic condition, con- tents, process as well as procedures. The kinematics computation model is established and analyzed.

A high-dexterity low-degree-of-freedom hybrid manipulator structure for robotic lion dance

Lion dance is a very popular and lively Chinese traditional art form.A robotic project in Singapore has been dedicated to the design and demonstration for similar traditional art forms using modern mechatronics technology.This paper deals with a novel six-degree-of-freedom (6-DOF) hybrid manipulator with high stiffness,high loading capability and high dexterity,mimicking the lion dancer's upper body motions along with the lion head movements.The design of the hybrid manipulator consists of a 2-DOF torso structure in serial configuration and a 4-DOF dual arm structure in parallel configuration.The combined 6-DOF hybrid manipulator can support the weight and dynamics of the lion head during the lion dance performance.Forward kinematics of the manipulator has been formulated and visualized for design purposes.Inverse kinematics of the hybrid manipulator were analytically derived for real-time motion control.Based on the design and modeling,a complete hybrid manipulator has been fabricated,implemented into the robotic lion,and successfully demonstrated for real robotic lion dance performance.

Bio-inspired Backstepping Adaptive Sliding Mode Control for Parallel Mechanism with Actuation Redundancy

This paper presents a bio-inspired backstepping adaptive sliding mode control strategy for a novel 3 degree of freedom(3-DOF) parallel mechanism with actuation redundancy. Based on the kinematic model and the dynamic model, a sliding mode controller is designed to assure the tracking performance, and an adaptive law is introduced to approximate the system uncertainty including parameters variation, external disturbances and un-modeled part. Furthermore, a bio-inspired model is introduced to solve the inherent chattering problem of sliding mode control and provide a chattering free control. The simulation and experimental results testify that the proposed bio-inspired backstepping adaptive sliding mode control can achieve better performance(the tracking accuracy,robustness, response speed, etc.) than the conventional slide mode control.

Dimensional Synthesis of a 3-DOF Parallel Manipulator with Full Circle Rotation

Parallel robots are widely used in the academic and industrial fields. In spite of the numerous achievements in the design and dimensional synthesis of the low-mobility parallel robots, few research efforts are directed towards the asymmetric 3-DOF parallel robots whose end-effector can realize 2 translational and 1 rotational（2T1R） motion. In order to develop a manipulator with the capability of full circle rotation to enlarge the workspace, a new 2T1 R parallel mechanism is proposed. The modeling approach and kinematic analysis of this proposed mechanism are investigated. Using the method of vector analysis, the inverse kinematic equations are established. This is followed by a vigorous proof that this mechanism attains an annular workspace through its circular rotation and 2 dimensional translations. Taking the first order perturbation of the kinematic equations, the error Jacobian matrix which represents the mapping relationship between the error sources of geometric parameters and the end-effector position errors is derived. With consideration of the constraint conditions of pressure angles and feasible workspace, the dimensional synthesis is conducted with a goal to minimize the global comprehensive performance index. The dimension parameters making the mechanism to have optimal error mapping and kinematic performance are obtained through the optimization algorithm. All these research achievements lay the foundation for the prototype building of such kind of parallel robots.

A large workspace flexure hinge-based parallel manipulator system

Parallel manipulator systems as promising precision devices are used widely in current researches. A novel large workspace flexure parallel manipulator system utilizing wide-range flexure hinges as passive joints is proposed in this paper, which can attain sub-micron-seale precision over the cubic centimeter motion range. This paper introduces the mechanical system architecture based on the wide-range flexure hinges, analyzes the kinematics via stiffness matrices, presents the control system configuration and control strategy, and finally gives the system performance test results.