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.

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.

CONCISE SOLUTION OF FORWARD KINEMATICS ANALYSIS OF PARALLEL MECHANISM IN 6-SPS SIMILAR PLATFORM

The forward kinematics analysis of a special 6-SPS Stewart platform is presented, in which both the base and the mobile platforms are hexagon and similar to each other. The forward kinematics of the parallel mechanism is a complicated nonlinear problem, however. there exists a class of parallel kinematics platforms that have the simplest forward kinematics. By introducing quaternion to represent the rotary transformation matrix and applying dual space method to eliminate the high degree polynomials, the forward kinematics can be expressed by a set of quadratic algebra equations, which decouple the position and the orientation of the mobile platform. The approach only requires solving one-variable quadratic equations. Besides, spurious complex roots are automatically avoided. Eight possible solutions are obtained from the approach. It discovers the inner symmetry relationship between the solutions of the forward kinematics.

Fast Numerical Solution to Forward Kinematics of General Stewart Mechanism Using Quaternion

The forward kinematics of the general Stewart mechanism is studied and a fast numerical method is presented.Quaternion is utilized to model the forward kinematics and the equations are merely a system of quadratic ones.The numerical method is a nice simplification of the Newton-Raphson method when applied to this system.A simulation of the movement control of the Stewart mechanism is accomplished,confirming the effectiveness of the proposed algorithm in real-time conditions.

The Kinematics Analysis of Heald Selecting Mechanism of Rotary Electronic Dobby

In order to improve the reliability of the mechanical movement of the rotary electronic dobby, the kinematics analysis of the heald selection mechanism is carried out and the simulation is carried out with Matlab. Firstly, the operation mechanism of the heald selection mechanism is analyzed in detail. The conjugate cam is mapped. The cam profile curve is fitted with cubic spline interpolation. Secondly, based on the overall analysis method and the complex vector method, the kinematics analysis of the key components after the high pair low generation is performed, and the angular displacement and angular velocity of each component are calculated with the rotation of the active cam. Finally, the movement curve diagram is drawn with Matlab, which lays the foundation for the dynamic analysis and in-depth study of the selection mechanism in the future.

Bionic Mechanism and Kinematics Analysis of Hopping Robot Inspired by Locust Jumping

A flexible-rigid hopping mechanism which is inspired by the locust jumping was proposed, and its kinematic characteris- tics were analyzed. A series of experiments were conducted to observe locust morphology and jumping process. According to classic mechanics, the jumping process analysis was conducted to build the relationship of the locust jumping parameters. The take-offphase was divided into four stages in detail. Based on the biological observation and kinematics analysis, a mechanical model was proposed to simulate locust jumping. The forces of the flexible-rigid hopping mechanism at each stage were ana- lyzed. The kinematic analysis using pseudo-rigid-body model was described by D-H method. It is confirmed that the proposed bionic mechanism has the similar performance as the locust hind leg in hopping. Moreover, the jumping angle which decides the jumping process was discussed, and its relation with other parameters was established. A calculation case analysis corroborated the method. The results of this paper show that the proposed bionic mechanism which is inspired by the locust hind limb has an excellent kinematics performance, which can provide a foundation for design and motion planning of the hopping robot.

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.

Mechanisms and Kinematics of Hydraulic Support for Top-Coal Caving

The structure and characteristic of new type of hydraulic support for top coal caving were discussed. The mechanism and kinematics of the hydraulic support were analyzed. The formulas were deduced to calculate the velocity and acceleration of top beam, shield beam, front and back legs, which give the solution to the design and research for hydraulic support.

Configuration and kinematics analysis of locking-releasing mechanism for side-loaded lunar rover

In order to save space for storing precision equipments,lower the center of mass of Lander and reduce lunar rover's dimension constraint limited by mechanism of Lander,the locking-releasing mechanism of side-loaded lunar rover loaded outside Lander is presented,which is a kind of metamorphic mechanism.To ensure the working of this mechanism as the metamorphic process designed,configuration analysis of the locking-releasing mechanism is carried out,and topological structures are described by Huston lower numbered arrays.A kinematic mathematical model of the mechanism is established through homogeneous transformation matrix.The kinematic simulation validates the feasibility of the locking-releasing mechanism when the configurations are shifted from one to the other.

Modeling and Kinematics Simulation of Hydro-mechanical Split Path Steering Device of Tracked Vehicle Based on CATIA

Based on the working principle of hydro-mechanical split path of tracked vehicle, a operating gear was developed which was controlled by steering wheel and match with transmission case. Then CATIA software was used to build the three-dimensional model and carry out dynamic simulation of the mechanism. The result indicates that the design of the mechanism fulfills the request.

The Kinematics and Force Analysis of a New Leg Mechanism for Multi-legged Wall-Climbing Robot

This paper presents a new kind of leg mechanism with which the wall climbing robot can easily perform the ground to wall transition by itself.To get its walking envelope and limit position,the forward/inverse kinematics and the statics of the mechanism are solved.All of these lay the foundation for ground to wall transition gait programing,mechanism parameter selection and optimization.

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.

Three-dimensional Geometry and Kinematics of the Changning Anticline in the Southern Sichuan Basin

In this study,we aim to clarify the structural characteristics and deformation process of the Changning anticline.We carefully interpret 38 two-dimensional(2D)seismic profiles in the study area and establish three-dimensional(3D)geometric and quantitative kinematic models of the Changning anticline.This study shows that the basement fault controls the formation of the Changning anticline.The fault slope of the main fault in the basement shows’steep in the upper and gentle in the lower’structural characteristics vertically,possessing obvious segmentary characteristics transversely and presents the overall characteristics of’steep in the east and gentle in the west’.Further analysis shows that the Changning anticline proceeds west and terminates at the boundary defined by current surface features but gradually disappears westward across the Mt.Huaying fault zone.Furthermore,we identified that deformation of the Changning anticline began during the early Yanshanian movement period.Under compressional stress from the southeast,the anticline slid forward along the basement fault until the end of the Yanshanian movement period,when the dominant WNW-ESE structure gradually emerged.Since the Himalayan movement period,a series of NE-trending structures have been formed in the anticline,owing to multi-directional compressive stress.

Kinematics and dynamics analysis of a 3-7R parallel decoupling mechanism

One kind of movable-pair analysis method is adopted to analyze the configuration of a 3-7R （revolute-pair） parallel decoupling mechanism, and the mechanism＇s characteristics are summarized. The mechanism has three orthogonal distributional branch-chains, and all movable pairs are rotational joints. The movable platform of the mechanism has x, y, z translational decoupling directions. Furthermore, in order to verify the mechanism＇s decoupling characteristics, the mechanism＇s kinematics analysis is solved, and the mechanism＇s direct/inverse kinematics model, input/output velocities and accelerations are deduced, which confirm its decoupling movement characteristics. Finally, one kind of mechanism link decomposed-integrated approach is adopted, and the mechanism＇s dynamics model is completed with the Lagrange method, which also proves its decoupling force characteristics. All of these works provide significant theory for the further study of the mechanism＇s control strategy, design, path planning etc.

;ast forward kinematics algorithm for real-time and ligh-precision control of the 3-RPS parallel mechanism

A new forward kinematics algorithm for the mechanism of 3-RPS （R： Revolute; P： Prismatic; S： Spherical） parallel manipulators is proposed in this study. This algorithm is primarily based on the special geometric conditions of the 3-RPS parallel mechanism, and it eliminates the errors produced by parasitic motions to improve and ensure accuracy. Specifically, the errors can be less than 10 6. In this method, only the group of solutions that is consistent with the actual situation of the platform is obtained rapidly. This algorithm substantially improves calculation efficiency because the selected initial values are reasonable, and all the formulas in the calculation are analytical. This novel forward kinematics algorithm is well suited for real-time and high-precision control of the 3-RPS parallel mechanism.

KINEMATICS FEATURE ANALYSIS OF A 3-DOF COMPLIANT MECHANISM FOR MICRO MANIPULATION

Kinematics and its related issues of a 3-DOF in-parallel compliant mechanismare focused on. The micro manipulation application that requires high accuracy is developed. Designof the developed micromanipulator is based on the modified Delta mechanism. The main advantages ofthis manipulator are the use of only revolute flexure hinges and the capability to produce puretranslation theoretically. The aim is to develop an efficient kinematic model used for positioningcontrol. For this purpose, the Jacobian matrix relating the end effector position with the actuatordisplacements is obtained by both theoretical derivation and experiment. Aiming at the abnormalityin the motion capabilities of the micromanipulator found in calibration experiment, the mobility ofthe compliant mechanism on a theoretical level is analyzed by using the matrix method and screwtheory. Both the experimental and theoretical results have verified that the compliant mechanismdoes have rotational motion.

Kinematics and Dynamics Analysis of a Quadruped Walking Robot with Parallel Leg Mechanism

It is desired to require a walking robot for the elderly and the disabled to have large capacity,high stiffness,stability,etc.However,the existing walking robots cannot achieve these requirements because of the weight-payload ratio and simple function.Therefore,Improvement of enhancing capacity and functions of the walking robot is an important research issue.According to walking requirements and combining modularization and reconfigurable ideas,a quadruped/biped reconfigurable walking robot with parallel leg mechanism is proposed.The proposed robot can be used for both a biped and a quadruped walking robot.The kinematics and performance analysis of a 3-UPU parallel mechanism which is the basic leg mechanism of a quadruped walking robot are conducted and the structural parameters are optimized.The results show that performance of the walking robot is optimal when the circumradius R,r of the upper and lower platform of leg mechanism are 161.7 mm,57.7 mm,respectively.Based on the optimal results,the kinematics and dynamics of the quadruped walking robot in the static walking mode are derived with the application of parallel mechanism and influence coefficient theory,and the optimal coordination distribution of the dynamic load for the quadruped walking robot with over-determinate inputs is analyzed,which solves dynamic load coupling caused by the branches’ constraint of the robot in the walk process.Besides laying a theoretical foundation for development of the prototype,the kinematics and dynamics studies on the quadruped walking robot also boost the theoretical research of the quadruped walking and the practical applications of parallel mechanism.

Kinematics Analysis and Optimization of the Fast Shearing-extrusion Joining Mechanism for Solid-state Metal

Dynamical Joining of the solid-state metal is the key technology to realize endless hot rolling. The heating and laser welding method both require long joining time. Based on super deformation method, a 7-bar and 2-slider mechanism was developed in Japan, and the joining time is less than 0.5 s, however the length of each bar are not reported and this mechanism is complex. A relatively simple 6-bar and 1-slider mechanism is put forward, which can realize the shearing and extrusion motion of the top and bottom blades with a speed approximately equal to the speed of the metal plates. In order to study the kinematics property of the double blades, based on complex vector method, the multi-rigid-body model is built, and the displacement and speed functions of the double blades, the joining time and joining thickness are deduced, the kinematics analysis shows that the initial parameters can＇t satisfy the joining process. Hence, optimization of this mechanism is employed using genetic algorithm（GA） and the optimization parameters of this mechanism are obtained, the kinematics analysis show that the joining time is less than 0.1 s, the joining thickness is more than 80% of the thickness of the solid-state metal, and the horizontal speeds of the blades are improved. A new mechanism is provided for the joining of the solid-state metal and a foundation is laid for the design of the device.

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.