scholarly journals Simultaneous Measurement Method and Error Analysis of Six Degrees of Freedom Motion Errors of a Rotary Axis Based on Polyhedral Prism

2021 ◽  
Vol 11 (9) ◽  
pp. 3960
Author(s):  
Dong Ma ◽  
Jiakun Li ◽  
Qibo Feng ◽  
Qixin He ◽  
Yaowen Ding ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Motion Error ◽  
Six Degrees Of Freedom ◽  
Rotary Axis ◽  
Position Errors ◽  
Manufacturing Errors ◽  
Polyhedral Prism ◽  
Novel Method ◽  
Six Dof ◽  
Geometric Motion

A novel method is proposed for measuring the six degrees-of-freedom (DOF) geometric motion errors of a rotary axis based on a polyhedral prism. An error-sensitive unit which consists of a polyhedral prism and a planar reflector, is designed to carry out measurement of all six DOF errors, including the angular positioning error, the tilt motion error around the Y axis, the tilt motion error around the X axis, the radial motion error along the X and Y axes, and the axial motion error along the Z axis. The mathematical error model, including the six DOF geometric motion errors of the rotary axis, the installation errors between the polyhedral prism and the rotary axis, the manufacturing errors of the polyhedral prism, and the position errors of the sensors, are established. The effectiveness of the proposed method and the compensation model was simulated and experimentally verified.

scholarly journals Simultaneous Measurement Method and Error Analysis of the Six Degrees-of-Freedom Motion Errors of a Rotary Axis

2018 ◽  
Vol 8 (11) ◽  
pp. 2232 ◽  
Author(s):  
Chuanchen Bao ◽  
Qibo Feng ◽  
Jiakun Li
Keyword(s):  
Simultaneous Measurement ◽  
Error Compensation ◽  
Degrees Of Freedom ◽  
Translational Motion ◽  
Laser Interferometry ◽  
Positioning Error ◽  
Motion Error ◽  
Measuring Device ◽  
Six Degrees Of Freedom ◽  
Rotary Axis

Error measurement of a rotary axis is the key to error compensation and to improving motion accuracy. However, only a few instruments can measure all the motion errors of a rotary axis. In this paper, a device based on laser collimation and laser interferometry was introduced for simultaneous measurement of all six degrees-of-freedom motion errors of a rotary axis. Synchronous rotation of the target and reference rotary axes was achieved by developing a proportional–integral–derivative algorithm. An error model for the measuring device was established using a homogeneous transformation matrix. The influences of installation errors, manufacturing errors, and error crosstalk were studied in detail, and compensation methods for them were proposed. After compensation, the repeatability of axial and radial motion errors was significantly improved. The repeatability values of angular positioning error and of tilt motion error around the y axis and x axis were 28.0″, 2.8″, and 3.9″. The repeatability values of translational motion errors were less than 2.8 μm. The comparison experiments show that the comparison errors of angular positioning error and tilt motion error around the y axis were 2.3″ and 2.9″, respectively. These results demonstrate the effectiveness of our method and the error compensation model.

Kinematic model to control the end-effector of a continuum robot for multi-axis processing

Robotica ◽  
2015 ◽  
Vol 35 (1) ◽  
pp. 224-240 ◽  
Author(s):  
Salvador Cobos-Guzman ◽  
David Palmer ◽  
Dragos Axinte
Keyword(s):  
Degrees Of Freedom ◽  
Kinematic Model ◽  
Euler Angle ◽  
Inverse Kinematic ◽  
End Effector ◽  
Six Degrees Of Freedom ◽  
Hazardous Environments ◽  
Continuum Robot ◽  
Novel Method ◽  
Six Dof

SUMMARYThis paper presents a novel kinematic approach for controlling the end-effector of a continuum robot for in-situ repair/inspection in restricted and hazardous environments. Forward and inverse kinematic (IK) models have been developed to control the last segment of the continuum robot for performing multi-axis processing tasks using the last six Degrees of Freedom (DoF). The forward kinematics (FK) is proposed using a combination of Euler angle representation and homogeneous matrices. Due to the redundancy of the system, different constraints are proposed to solve the IK for different cases; therefore, the IK model is solved for bending and direction angles between (−π/2 to +π/2) radians. In addition, a novel method to calculate the Jacobian matrix is proposed for this type of hyper-redundant kinematics. The error between the results calculated using the proposed Jacobian algorithm and using the partial derivative equations of the FK map (with respect to linear and angular velocity) is evaluated. The error between the two models is found to be insignificant, thus, the Jacobian is validated as a method of calculating the IK for six DoF.

scholarly journals A Method for Simultaneously Measuring 6DOF Geometric Motion Errors of Linear and Rotary Axes Using Lasers

Sensors ◽  
2019 ◽  
Vol 19 (8) ◽  
pp. 1764 ◽  
Author(s):  
Zheng ◽  
Feng ◽  
Zhang ◽  
Li
Keyword(s):  
Measurement System ◽  
Degrees Of Freedom ◽  
High Efficiency ◽  
Single Mode ◽  
Cnc Machine Tools ◽  
Laser Source ◽  
Cnc Machine ◽  
Motion Error ◽  
Rotary Axis ◽  
Geometric Motion

A novel method for simultaneously directly measuring six-degrees-of-freedom (6DOF) geometric motion errors of CNC machine tools was proposed, and a corresponding measurement system was developed. This method can not only be applied for measuring a linear axis, but also for a rotary axis. A single-mode fiber was used to separate the measuring unit from the laser source in order to ensure system thermal stability and measurement accuracy. The method has the advantages of high efficiency and good accuracy, and requires no complicated decoupling calculation. The positioning error of the linear axis and radial motion error of the rotary axis are measured by laser interferometry and other 5DOF geometric motion errors by laser collimation. A series of experiments were performed to verify the feasibility and effectiveness of the developed measurement system.

Dynamics Simulation of a Six-DOF Tunnel Segment Erector for Tunnel Boring Machine Based on Virtual Prototype

2012 ◽  
Vol 251 ◽  
pp. 231-234
Author(s):  
Gang Li ◽  
Ya Dong Chen ◽  
Bo Wang ◽  
Wan Shan Wang
Keyword(s):  
Degrees Of Freedom ◽  
Tunnel Boring Machine ◽  
Virtual Prototype ◽  
Dynamics Simulation ◽  
Design Parameters ◽  
Six Degrees Of Freedom ◽  
Tunnel Boring ◽  
Six Dof ◽  
Freedom Movement ◽  
Segment Erector

In this paper, we present the modeling and dynamics simulation of a six-DOF tunnel segment erector for tunnel boring machine (TBM), which is performed in the virtual prototype platform. The 3D virtual assembling model of a tunnel segment erector is built based on Pro/E software according to its design parameters such as structure and size. After the interference inspection, the model is imported into ADAMS through the interface module of Mech/Pro. The model is simplified and optimized reasonably and various constraints are applied under variety working conditions. The results of simulation show that the design has six degrees of freedom movement capacity which meets the design requirements. At the same time the dynamics characteristics of drives and the forces of each part are obtained and they will provide a boundary condition for strength check and basis for the power system design which is important for the further optimal design.

General inverse solution of six-degrees-of-freedom serial robots based on the product of exponentials model

2018 ◽  
Vol 38 (3) ◽  
pp. 361-367 ◽  
Author(s):  
Haixia Wang ◽  
Xiao Lu ◽  
Wei Cui ◽  
Zhiguo Zhang ◽  
Yuxia Li ◽  
...  
Keyword(s):  
Design Methodology ◽  
Degrees Of Freedom ◽  
Screw Theory ◽  
Complex Problem ◽  
Content Type ◽  
Geometrical Properties ◽  
Closed Form Solutions ◽  
Six Degrees Of Freedom ◽  
Serial Robots ◽  
Six Dof

Purpose Developing general closed-form solutions for six-degrees-of-freedom (DOF) serial robots is a significant challenge. This paper thus aims to present a general solution for six-DOF robots based on the product of exponentials model, which adapts to a class of robots satisfying the Pieper criterion with two parallel or intersecting axes among its first three axes. Design/methodology/approach The proposed solution can be represented as uniform expressions by using geometrical properties and a modified Paden–Kahan sub-problem, which mainly adopts the screw theory. Findings A simulation and experiments validated the correctness and effectiveness of the proposed method (general resolution for six-DOF robots based on the product of exponentials model). Originality/value The Rodrigues rotation formula is additionally used to turn the complex problem into a solvable trigonometric function and uniformly express six solutions using two formulas.

scholarly journals Trueness of full-arch IO scans estimated based on 3D translational and rotational deviations of single teeth—an in vitro study

2021 ◽  
Author(s):  
Johanna Radeke ◽  
Annike B. Vogel ◽  
Falko Schmidt ◽  
Fatih Kilic ◽  
Stefan Repky ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
In Vitro Study ◽  
Confocal Laser ◽  
Anterior Crowding ◽  
Six Degrees Of Freedom ◽  
Staff Members ◽  
Total Displacement ◽  
Dental Staff ◽  
Novel Method

Abstract Objectives To three-dimensionally evaluate deviations of full-arch intraoral (IO) scans from reference desktop scans in terms of translations and rotations of individual teeth and different types of (mal)occlusion. Materials and methods Three resin model pairs reflecting different tooth (mal)positions were mounted in the phantom head of a dental simulation unit and scanned by three dentists and three non-graduate investigators using a confocal laser IO scanner (Trios 3®). The tooth-crown surfaces of the IO scans and reference scans were superimposed by means of best-fit alignment. A novel method comprising the measurement of individual tooth positions was used to determine the deviations of each tooth in the six degrees of freedom, i.e., in terms of 3D translation and rotation. Deviations between IO and reference scans, among tooth-(mal)position models, and between dentists and non-graduate investigators were analyzed using linear mixed-effects models. Results The overall translational deviations of individual teeth on the IO scans were 76, 32, and 58 µm in the lingual, mesial, and intrusive directions, respectively, resulting in a total displacement of 114 µm. Corresponding rotational deviations were 0.58° buccal tipping, 0.04° mesial tipping, and 0.14° distorotation leading to a combined rotation of 0.78°. These deviations were the smallest for the dental arches with anterior crowding, followed by those with spacing and those with good alignment (p < 0.05). Results were independent of the operator’s level of education. Conclusions Compared to reference desktop scans, individual teeth on full-arch IO scans showed high trueness with total translational and rotational deviations < 115 µm and < 0.80°, respectively. Clinical relevance Available confocal laser IO scanners appear sufficiently accurate for diagnostic and therapeutic orthodontic applications. Results indicate that full-arch IO scanning can be delegated to non-graduate dental staff members.

Kinematics of the Translational 3-URC Mechanism1

2004 ◽  
Vol 126 (6) ◽  
pp. 1113-1117 ◽  
Author(s):  
Raffaele Di Gregorio
Keyword(s):  
Explicit Form ◽  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Industrial Applications ◽  
Parallel Architectures ◽  
Six Degrees Of Freedom ◽  
Spatial Mechanisms ◽  
Six Dof ◽  
And Control ◽  
Spherical Motion

The use of less than six degrees of freedom (dof) mechanisms instead of six-dof ones is always recommended when the application makes it possible, since their architectures and control are simpler to manufacture and implement respectively. Three-dof mechanisms constitute an important subset of less-than-six-dof mechanisms, since either translational or spherical motion can be obtained through three-dof spatial mechanisms and many industrial applications require the only translational or spherical motion. This paper presents a new translational parallel mechanism (TPM), named translational 3-URC. The new mechanism belongs to the parallel architectures with 3-URC topology, which contain another architecture that is a spherical parallel wrist. The proposed TPM is not overconstrained and has three equal legs whose kinematic pairs are three revolute pairs and one passive cylindrical pair per leg. Its actuated pairs are three revolute pair located on the frame. The position and velocity analyses of the translational 3-URC will be addressed and solved. Its singularity conditions will be written in explicit form and geometrically interpreted.

scholarly journals THE EFFECT OF COLLATERAL LIGAMENT INJURY ON CARTILAGE CONTACT IN KNEE JOINTS MODELED WITH SIX DEGREES OF FREEDOM

2016 ◽  
Vol 16 (03) ◽  
pp. 1650080
Author(s):  
NERIMAN ÖZADA
Keyword(s):  
Knee Joint ◽  
Degrees Of Freedom ◽  
Contact Point ◽  
Kinematic Model ◽  
Surface Geometry ◽  
Collateral Ligament ◽  
Point Distribution ◽  
Six Degrees Of Freedom ◽  
Six Dof ◽  
Intact Knee

The purpose of this study was to create a kinematic model of the knee joint with six degrees of freedom (DOF) and evaluate the effect of medial collateral ligament (MCL) and lateral collateral ligament (LCL) rupture on cartilage contact point distribution on the tibia during flexion. We hypothesized that collateral ligament contributions vary over six DOF of knee joint articulation and affect the cartilage contact point distribution during joint articulation. The ligament contributions and distribution of joint cartilage contact points cannot be fully assessed with simplified joint models or invasive experiments. Therefore, we developed a new model in which the tibia and femur centers of mass were determined from their surface geometry, and the displacement of the moving tibia was determined from the displacements of the attached ligaments. Compared to the intact knee, the tibia with the LCL removed had higher medial translation and lower valgus rotation. The tibia with the MCL removed had higher lateral translation and higher valgus rotation than the intact knee. At 0[Formula: see text], 30[Formula: see text], and 60[Formula: see text], the tibia with the LCL removed had more internal rotation than the intact knee. Understanding six DOF knee joint kinematics with integration of ligament contributions and cartilage contact positions is useful for the diagnosis of ligament injuries and the design of articulating surfaces for total arthroplasty.

scholarly journals The Effect of Manufacturing Quality on Rocket Precision

Aerospace ◽  
2021 ◽  
Vol 8 (6) ◽  
pp. 160
Author(s):  
Zvonko Trzun ◽  
Milan Vrdoljak ◽  
Hrvoje Cajner
Keyword(s):  
Monte Carlo Simulation ◽  
Manufacturing Process ◽  
Degrees Of Freedom ◽  
Cad Model ◽  
Impact Point ◽  
High Quality ◽  
Six Degrees Of Freedom ◽  
Manufacturing Quality ◽  
3D Cad ◽  
Manufacturing Errors

The effect of manufacturing quality on rocket impact point dispersion is analyzed. The approach presented here applies to any type of rocket. Here, manufacturing quality is demonstrated for the unguided rocket, and by simulating four typical manufacturing errors: erroneously manufactured warhead, misalignment between the warhead and engine chamber, asymmetrically installed propellant, and error in nozzle manufacturing. A new methodology is proposed, which combines a 3D CAD model of the asymmetrical projectile (due to manufacturing errors) and the improved Six-degrees-of-freedom (6DOF) model of its flight into a comprehensive Monte-Carlo simulation. In that way, the rocket trajectory dispersion is correlated directly to the imperfection of the manufacturing process. Three quality levels are simulated (low, standard, and high quality), and each of the analyzed manufacturing errors depends on the chosen quality. The results show how important it is to impose the highest quality on nozzle manufacturing, and if this condition is not met, reveal if strict tolerances applied to other steps of the manufacturing process can compensate for the consequential drop of precision.

Modeling and prototype experiment of a six-DOF parallel micro-manipulator with nano-scale accuracy

2014 ◽  
Vol 229 (14) ◽  
pp. 2611-2625
Author(s):  
Yi Dong ◽  
Feng Gao ◽  
Yi Yue
Keyword(s):  
Degrees Of Freedom ◽  
Experimental Result ◽  
Element Analysis ◽  
Six Degrees Of Freedom ◽  
Compliant Structure ◽  
Nano Scale ◽  
Stiffness Model ◽  
Micro Manipulator ◽  
Six Dof ◽  
The Relationship

This paper presents a high-accurate micro-manipulator featured with monolithic compliant structure, orthogonally arranged parallel mechanism and piezoelectric (PZT) actuation. 6-SPS mechanism is employed to provide six degrees of freedom (DOF), including three linear translations and three rotations. The kinematics and stiffness of the micro-manipulator is studied first in this paper. Then, the relationship between PZT nominal displacement and the end pose is derived. Aiming at achieving trajectories with nano-scale accuracy, a two-step strategy is proposed. Finite element analysis (FEA) is conducted to verify the kinematics and stiffness model. Finally, in order to demonstrate the performance of the micro-manipulator, experiments of typical trajectories are carried out. The experimental result shows that the proposed micro-manipulator is capable of achieving trajectories with nano-scale accuracy.

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