Forward Kinematics Equations Research Articles

A kinematic calibration method of a 3-DOF secondary mirror of the giant magellan telescope based on least square algorithm

Because of manufacturing and assembly errors in the geometric parameters of parallel robots, calibrating the parameters is necessary for improving the positioning accuracy. The objective of this study is a 3-DOF secondary mirror of the giant Magellan telescope, which is operated by a 3-DOF parallel robot. In this paper, a kinematic calibration method is presented. In this method, a moving platform is commanded to execute a sinusoidal movement by the cooperation of three piezoelectric actuators, and experimental data is obtained using capacitive sensors. The inverse kinematic and forward kinematic equations for the local system are illustrated in this paper. Furthermore, importantly, a least square algorithm is implemented to reduce the residual between the experimental values and expected values. Additionally, a simulation model is developed for supervising the movement of the system. Results of experiment show that the method used in this paper is effective and efficient.

A geometric postprocessing method for 5-axis machine tools using locations of joint points

We present a postprocessing algorithm for 5-axis machines, which can be applied to types with two rotary axes (2R-3L) and three rotary axes (3R-2L). Five-axis machining requires a postprocessor for converting cutter-location (CL) data to numerical-control (NC) data. The existing methods for postprocessing use inverse kinematics equations from the forward kinematics. However, for 5-axis machines with three rotary axes, the inverse kinematics equations cannot be induced directly, because the forward kinematics equations are coupled. To derive the joint values from the forward kinematics equations, previous algorithms use iterative numerical methods for the postprocessing; this requires a search algorithm with much computation time and may fail to obtain a solution. Our algorithm has three advantages: first, the forward kinematics equations are not required; second, the method is reliable and eliminates the need for numerical methods for the inverse kinematics, which results in exact solutions; and finally, the proposed algorithm is generic for 5-axis machines, which can also be applied to 2R-3L 5-axis machines.

The Analysis and Research of Hedge Trimmer Robotics about Manipulator Kinematics

According to the analysis theory of the four freedom degree about the robots mechanical arm, in this paper established the four freedom degree of the mechanical arm forward and inverse kinematics equation, which was based on the coordinate system, giving the relationship of the spatial location and gesture between movement member and end executor. Besides, it could solve its Jacobian matrix, and provide theoretical basis to achieve the velocity control program on the end of mechanical arm in Cartesian space. The application of ADAMS had carried out the simulation, analysed the location and movement relations among the mechanical structure, which provided significant data for the actual hedge trimming operation.

Theoretical Analysis of Mechanism Kinematics for Boom Crane of Marine Drilling Platform

The boom crane of marine drilling platform is an important part of the automated pipe racking system. It has important engineering significance to study the kinematics of boom crane for the automatic control and accurate positioning. Using the method of robot mechanisms, the kinematics of mechanism for boom crane on marine drilling platform is discussed in this paper. According to the structure and motion characteristics of the boom crane, a special joint coordinate system is chosen. The kinematics model of the boom crane is established. The forward kinematics equations, inverse kinematics calculation formulas are derived. The correctness of formulas is verified by examples. The theoretical basis is provided for the movement automatic control and subsequent dynamics and boom crane mechanics analysis when considering the elastic deformation.

Kinematic analyses of novel translational parallel manipulators

This study reports on the kinematic analyses of four translational parallel manipulators (3RPC, SPS + 2RPC, RPPR + 2RPC and RPPR + 2PPP) articulated with linear actuators. They are based on serially connected chains which are connected with cylindrical (C), prismatic (P), revolute (R), spherical (S) and universal (U) joints. Of these manipulators, the one which is a fully decoupled, fully isotropic and singularity-free translational parallel manipulator (RPPR+2PPP) offers a one-to-one correspondence between its input and output displacement. This makes its forward and inverse position analyses simpler with a set of linear equations to be solved. Although the other manipulators have coupled kinematics, they still have simpler forward kinematic equations over other well-known translational parallel manipulators reported in the literature. We also employ screw theory to undertake the velocity and acceleration analyses. The primary contribution of this manuscript is to show how the 3-RPC translational parallel manipulator can be gradually modified in order to obtain a fully isotropic, fully decoupled and singularity-free translational parallel manipulator.

Bioinspired Sinusoidal Finger Joint Synergies for a Dexterous Robotic Hand to Screw and Unscrew Objects With Different Diameters

This paper addresses the complex task of unscrewing and screwing objects with a dexterous anthropomorphic robotic hand in two cases: with the first finger and thumb and also with the little finger and thumb. To develop an anthropomorphic solution, human finger synergies from nine test subjects were recorded while unscrewing and screwing a threaded cap. Human results showed that the periodic motions exhibited by the finger joints shared a common frequency for each subject, but differed in amplitude and phase. From the gathered data, a set of sinusoidal trajectories were developed to approximate this motion for application to a robotic hand. Because the joint trajectories exhibited the same frequency, a family of sinusoids that share a common time vector can be used in the path planning of the robotic hand to unscrew and screw objects. Additionally, the human unscrewing data are highly similar to the mirror image of the screwing data. This chiastic trait enables screwing to be performed by decreasing the time vector; increasing the time vector produces unscrewing. These factors significantly reduce the computational cost and complexity of the task. Cartesian and joint space error analyses show that the developed sinusoidal trajectories closely mimic the motion profiles seen in the human experiments. Furthermore, this bioinspired sinusoidal solution is extended to objects with wide variations in diameters by relating joint angle offsets of the robotic hand to object diameter size through the forward kinematics equations. The sinusoidal trajectories are all implemented within a PID sliding mode controller for a dexterous artificial hand to ensure overall system stability. Using the bioinspired sinusoidal joint angle trajectories, the robotic hand successfully unscrewed and screwed four different objects in all trials conducted with each object diameter size.

Dynamic Modeling and Analysis of Lifting Mechanism for Forging Manipulator

The kinematic and dynamic behaviors of lifting mechanism for a forging manipulator are investigated. The forward kinematic equations are established. Then, based on the modular approach combined with equivalent dynamic ideal, the dynamic equations are deduced. Moreover, all the equations have been verified by the simulation on a virtual prototype with the ADAMS software and the experiments on a forging manipulator. The results show that the calculated values are well in agreement with the real measurements. Finally, both kinematic and dynamic models are analyzed, and it is found that the force produced by the kinetic energy has very weak effect on the results in comparison with the gravity. The results provide the foundation of gripper’s position control in automatic open-die forging process.

Study on Error Analysis of Parallel Machine Tool Based on Monte-Carlo Method

Aiming at the complexity of the parallel machine tool error assessment, the distance between the ball joints on the execution platform is considered as the constraint condition to establish the forward kinematic equation, and a mathematic model of space position and attitude errors is established. The paper proposes a method to the error analysis of the parallel machine tool based on Monte-Carlo simulation according to the structure characteristic, and gives a universal computation program. The feasibility of the method is verified by comparing with the traditional motion vector equation differential method in final.

Modeling and analysis of servo dynamics errors on measuring paths of five-axis machine tools

Dynamic error is one of the major error sources for five-axis machine tools in achieving high-speed machining. It can be estimated and compensated by means of servo dynamics modeling and servo control method. This paper presents a contour error model on five-axis measuring paths where the dynamics and contour errors of the tool center point (TCP) can be estimated accurately during five-axis synchronized motions. The forward and inverse kinematics equations are derived according to the kinematic configuration of a C-type five-axis machine. To generate smooth measuring paths, the S-shape acceleration/deceleration (ACC/DEC) method is applied on planning the motion trajectory. The contour error model of the TCP is derived by substituting the commands of the measuring trajectory into the servo dynamics models. To investigate how the contour charts of the TCP are affected by the dynamic gains of five-axis servo loops, twelve combinations under different gains are studied. It is shown that, for the CK2 path, the steady-state contour error consists of an offset and a double-circular trajectory which is quite different from that of two-axis contour path. By tuning the gains of the servo loops, the dynamics mismatch among five axes can be eliminated and the contour error of the TCP (CETCP) can be reduced. To validate the contour error equations, simulations and experiments are performed to demonstrate that the proposed method improves the contouring performance of the TCP significantly when performing five-axis synchronized motions.

Design and simulation for a hydraulic actuated quadruped robot

This paper describes the mechanical configuration of a quadruped robot firstly. Each of the four legs consists of three rotary joints. All joints of the robot are actuated by linear hydraulic servo cylinders. Then it deduces the forward and inverse kinematic equations for four legs with D-H transformation matrices. Furthermore, it gives a composite foot trajectory composed of cubic curve and straight line, which greatly reduces the velocity and acceleration fluctuations of the torso along forward and vertical directions. Finally, dynamics cosimulation is given with MSC.ADAMS and MATLAB. The results of co-simulation provide important guidance to mechanism design and parameters preference for the linear hydraulic servo cylinders.

Kinematic analysis of a 5-DOF hybrid-driven MR compatible robot for minimally invasive prostatic interventions

SUMMARYThis paper introduces the design and kinematic analysis of a 5-DOF (multiple degree of freedom) hybrid-driven MR (Magnetic Resonance) compatible robot for prostate brachytherapy. It can slip the leash of template and rely on the high precise of MR imaging. After a brief introduction on design requirements of MR compatible robot, a description of our robot structure, material selection, hybrid-driven, and control architecture are presented. Secondly, the forward kinematics equations are obtained according to the equivalent diagram of this robot, and the actual workspace can be outlined. This will help the designer to determine whether this robot can be operated in the MR core without intervention with patient. And then, the inverse kinematics equations combined with trajectory planning are used to calculate the actuators movement. This will help the control system to manipulate the robotic accurately. Finally, vision based experiments on phantoms are used to verify the mechanism precision. As the results shown, the needle tip precision of mechanism is 0.9 mm in the general lab environment.

A Comparative Study of Three Inverse Kinematic Methods of Serial Industrial Robot Manipulators in the Screw Theory Framework

In this paper, we compare three inverse kinematic formulation methods for the serial industrial robot manipulators. All formulation methods are based on screw theory. Screw theory is an effective way to establish a global description of rigid body and avoids singularities due to the use of the local coordinates. In these three formulation methods, the first one is based on quaternion algebra, the second one is based on dual-quaternions, and the last one that is called exponential mapping method is based on matrix algebra. Compared with the matrix algebra, quaternion algebra based solutions are more computationally efficient and they need less storage area. The method which is based on dual-quaternion gives the most compact and computationally efficient solution. Paden-Kahan sub-problems are used to derive inverse kinematic solutions. 6-DOF industrial robot manipulator's forward and inverse kinematic equations are derived using these formulation methods. Simulation and experimental results are given.

Ubiquitous Human Upper-Limb Motion Estimation using Wearable Sensors

Human motion capture technologies have been widely used in a wide spectrum of applications, including interactive game and learning, animation, film special effects, health care, navigation, and so on. The existing human motion capture techniques, which use structured multiple high-resolution cameras in a dedicated studio, are complicated and expensive. With the rapid development of microsensors-on-chip, human motion capture using wearable microsensors has become an active research topic. Because of the agility in movement, upper-limb motion estimation has been regarded as the most difficult problem in human motion capture. In this paper, we take the upper limb as our research subject and propose a novel ubiquitous upper-limb motion estimation algorithm, which concentrates on modeling the relationship between upper-arm movement and forearm movement. A link structure with 5 degrees of freedom (DOF) is proposed to model the human upper-limb skeleton structure. Parameters are defined according to Denavit-Hartenberg convention, forward kinematics equations are derived, and an unscented Kalman filter is deployed to estimate the defined parameters. The experimental results have shown that the proposed upper-limb motion capture and analysis algorithm outperforms other fusion methods and provides accurate results in comparison to the BTS optical motion tracker.

Wearable sensors for 3D upper limb motion modeling and ubiquitous estimation

Human motion capture technologies are widely used in interactive game and learning, animation, film special effects, health care, and navigation. Because of the agility, upper limb motion estimation is the most difficult problem in human motion capture. Traditional methods always assume that the movements of upper arm and forearm are independent and then estimate their movements separately; therefore, the estimated motion are always with serious distortion. In this paper, we propose a novel ubiquitous upper limb motion estimation method using wearable microsensors, which concentrates on modeling the relationship of the movements between upper arm and forearm. Exploration of the skeleton structure as a link structure with 5 degrees of freedom is firstly proposed to model human upper limb motion. After that, parameters are defined according to Denavit-Hartenberg convention, forward kinematic equations of upper limb are derived, and an unscented Kalman filter is invoked to estimate the defined parameters. The experimental results have shown the feasibility and effectiveness of the proposed upper limb motion capture and analysis algorithm.

DESIGN AND MANUFACTURE A 5 DOFCOORDINATE MEASURING ARM

The 5 DOF coordinate measuring arm is an equipment used to determine the coordinate of points in 3D space at the tangent point of the probe and object. The calculating of the coordinate at the tip of the probe is based on forward kinematic equation of a 5 DOF robot arm, by defining the transpose of the 5 knuckles. Accordingly, we can calculate and measure some geometric elements, such as distance, angle...rebuild surface of object and store data in files. So that, the equipment can be applied in many fieldS: measuring, examining, molding, reverse engineering…

Kinematics Analysis and Simulation of a Quadruped Robot

This paper presents the mechanical configuration of a quadruped robot with 4 rotary joints per leg firstly. All joints of the robot are activated by 16 identical hydraulic servo cylinders. Then it gives the forward and inverse kinematic equations of one leg with D-H transformation matrix. Furthermore, it also gives the jacobian matrix of the legs. The jacobian matrix establishes the relationships between the angle velocities of the 4 joints of the supporting leg and the moving velocity of the robot trunk. Lastly, a simple trot gait simulation is given based on MSC.ADAMS under the assumption that there are no slippages between the supporting feet and the ground.

An adaptive niching genetic algorithm approach for generating multiple solutions of serial manipulator inverse kinematics with applications to modular robots

SUMMARYInverse kinematics (IK) is a nonlinear problem that may have multiple solutions. A modified genetic algorithm (GA) for solving the IK of a serial robotic manipulator is presented. The algorithm is capable of finding multiple solutions of the IK through niching methods. Despite the fact that the number and position of solutions in the search space depends on the position and orientation of the end-effector as well as the kinematic configuration (KC) of the robot, the number of GA parameters that must be set by a user are limited to a minimum through the use of an adaptive niching method. The only requirement of the algorithm is the forward kinematics (FK) equations which can be easily obtained from the Denavit–Hartenberg link parameters and joint variables of the robot. For identifying and processing the outputs of the proposed GA, a modified filtering and clustering phase is also added to the algorithm. For the postprocessing stage, a numerical IK solver is used to achieve convergence to the desired accuracy. The algorithm is validated on three KCs of a modular and reconfigurable robot (MRR).

Design and forward kinematics of the compliant micro-manipulator with lever mechanisms

This paper presents the forward kinematics of a five-bar compliant micro-manipulator. To overcome the limited displacement of such a flexure-based mechanism driven by piezoelectric actuators, lever mechanisms are utilized to enlarge the working range. The mechanical design of the micro-manipulator is firstly described. Mathematical formulations for the five-bar mechanism are described and the solutions are developed to decide the end-effector position in Cartesian space. The amplification factor of the lever mechanism is also derived based on the analytical solution of the four-bar linkages. The velocity of the end-effector is obtained by differentiating the forward position kinematic equation, and the local mobility index of the five-bar compliant mechanism is determined and analysed. Based on linearization of trigonometric functions and constant Jacobian matrix, numerical simulations are carried out to investigate the performance of the five-bar compliant manipulator and to determine the optimal geometric parameters for the configuration. The comparisons between the exact solution and simplified methodologies are conducted. Experiments are carried out to validate the established model and the performance of the developed micro-manipulator.

Kinematic analysis of a serial–parallel machine tool: The VERNE machine

The paper derives the inverse and the forward kinematic equations of a serial–parallel 5-axis machine tool: the VERNE machine. This machine is composed of a three-degree-of-freedom (DOF) parallel module and a two-DOF serial tilting table. The parallel module consists of a moving platform that is connected to a fixed base by three non-identical legs. These legs are connected in a way that the combined effects of the three legs leadver-constrained mechanism with complex motion. This motion is defined as a simultaneous combination of rotation and translation. In this paper we propose symbolical methods that able to calculate all kinematic solutions and identify the acceptable one by adding analytical constraint on the disposition of legs of the parallel module.

Design of reconfigurable coupled-serial-chain-based manipulation assistive aids

Our goal is to design a reconfigurable single degree-of-freedom (dof) articulated manipulation assistive aid, whose end-effector is required to closely approximate a series of constrained planar paths. To this end, we investigate the viability of the coupled-serial-chain configuration manipulator design created by constraining the relative rotations of a revolute-jointed serial-chain manipulator with linear cable–pulley couplings. The forward kinematics equations take the form of a finite trigonometric series in terms of the input crank rotations. Our proposed Fourier-based synthesis method exploits this special structure to facilitate the design synthesis of such manipulators. We then examine design enhancements, to permit this manipulator to be reconfigured for multiple sets of constrained end-effector tasks, by controlled variation of the principal structural parameters. Particular attention is paid to the creation of a physical prototype, which facilitates such reconfiguration.