Analyses of Error and Precision of 6-DOF Platform

2012 ◽  
Vol 591-593 ◽  
pp. 2081-2086 ◽  
Author(s):  
Rui Ren ◽  
Chang Chun Ye ◽  
Guo Bin Fan
Keyword(s):  
Inverse Kinematics ◽  
Newton Iteration ◽  
Forward Kinematics ◽  
Parallel Mechanisms ◽  
End Effector ◽  
C Programming Language ◽  
C Programming ◽  
Manufacturing Tolerances ◽  
Parallel Robotics ◽  
Forward Kinematic

A particular subset of 6-DOF parallel mechanisms is known as Stewart platforms (or hexapod). Stewart platform characteristic analyzed in this paper is the effect of small errors within its elements (strut lengths, joint placement) which can be caused by manufacturing tolerances or setting up errors or other even unknown sources to end effector. The biggest kinematics problem is parallel robotics which is the forward kinematics. On the basis of forward kinematic of 6-DOF platform, the algorithm model was built by Newton iteration, several computer programs were written in the MATLAB and Visual C++ programming language. The model is effective and real-time approved by forwards kinematics, inverse kinematics iteration and practical experiment. Analyzing the resource of error, get some related spectra map, top plat position and posture error corresponding every error resource respectively. By researching and comparing the error spectra map, some general results is concluded.

scholarly journals Design and Implementation of 6 DOF ROTARIC Robot Using Inverse Kinematics Method

2021 ◽  
Vol 13 (2) ◽  
pp. 125-134
Author(s):  
Fransisko Limanuel ◽  
Calvin Susanto ◽  
Ferry Rippun Gideon Manalu
Keyword(s):  
Inverse Kinematics ◽  
Inverse Kinematic ◽  
Intersection Point ◽  
Forward Kinematics ◽  
End Effector ◽  
Work Area ◽  
Kinematic Method ◽  
Point Equation ◽  
Articulated Robot ◽  
Forward Kinematic

This paper will discuss the calculation of inverse kinematic which will be used to control the 6-DOF articulated robot. This robot consists of 6 Dynamixel MX-28 smart servo with OpenCM 9.04 microcontroller. The articulated robot has been simplified to 4-DOF because there are no obstacles in the work area and no special movements are required. The calculation method uses the intersection point equation between the ball and the line, so that it can make it easier to determine the point in calculating the kinematic inverse. The experiment is carried out using the desired position as input for the kinematic inverse to produce the angle of each joint. From the angle of each joint obtained, it will be entered into forward kinematic so that the end-effector position will be obtained. The desired position will be compared with the end-effector position, and then how much difference will be calculated. From the experimental results, it was found that the inverse kinematic method which has been inverted by the forward kinematic produces the same final position. Keywords: 6-DOF manipulator, Articulated robot, inverse kinematics and forward kinematics, Dynamixel MX-28, OpenCM 9

scholarly journals Inverse and Forward Kinematic Analysis of a 6-DOF Parallel Manipulator Utilizing a Circular Guide

Robotics ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 31
Author(s):  
Alexey Fomin ◽  
Anton Antonov ◽  
Victor Glazunov ◽  
Yuri Rodionov
Keyword(s):  
Kinematic Analysis ◽  
Inverse Kinematics ◽  
Parallel Manipulator ◽  
Forward Kinematics ◽  
Rotational Angle ◽  
End Effector ◽  
Kinematic Chains ◽  
Position And Orientation ◽  
Manipulator Design ◽  
Forward Kinematic

The proposed study focuses on the inverse and forward kinematic analysis of a novel 6-DOF parallel manipulator with a circular guide. In comparison with the known schemes of such manipulators, the structure of the proposed one excludes the collision of carriages when they move along the circular guide. This is achieved by using cranks (links that provide an unlimited rotational angle) in the manipulator kinematic chains. In this case, all drives stay fixed on the base. The kinematic analysis provides analytical relationships between the end-effector coordinates and six controlled movements in drives (driven coordinates). Examples demonstrate the implementation of the suggested algorithms. For the inverse kinematics, the solution is found given the position and orientation of the end-effector. For the forward kinematics, various assembly modes of the manipulator are obtained for the same given values of the driven coordinates. The study also discusses how to choose the links lengths to maximize the rotational capabilities of the end-effector and provides a calculation of such capabilities for the chosen manipulator design.

Inverse Kinematics of Discretely-Actuated Manipulators Within a Bounded Grid Element

2006 ◽  
Author(s):  
Deanne C. Kemeny ◽  
Raymond J. Cipra
Keyword(s):  
Inverse Kinematics ◽  
Lower Cost ◽  
Robotic Manipulators ◽  
Forward Kinematics ◽  
End Effector ◽  
Grid Element ◽  
The Third ◽  
Inverse Kinematics Problem

Discretely-actuated manipulators are defined in this paper as serial planar chains of many links and are an alternative to traditional robotic manipulators, where continuously variable actuators are replaced with discrete, or digital actuators. Benefits include reduced weight and complexity, and predictable manipulation at lower cost. Challenges to using digital manipulators are the discrete end-effector positions which make the inverse kinematics problem difficult to solve. Furthermore, for a specific application position in the manipulator workspace, there may not be an actual end-effector position. This research has relaxed the inverse kinematics problem around this challenge making each application position an element of a grid in which the end effector must reach. There may be many possible end-effector positions that would reach the element goal, the solution uses the first one that is found. The inverse kinematics solution assumes the assembly configuration of the digital manipulator is already solved specifically for the application grid. The Jacobian function, normally used to solve joint velocities, can be used to identify the exact shift vectors that are used for the inverse kinematics. Three methods to solve this problem are discussed and the third method was implemented as a four-part solution that is a directed and manipulated search for the inverse kinematics solution where all four solutions may be needed. A discussion of forward kinematics and the Jacobian function in relation to digital manipulators is also presented.

Kinematics Analysis of a Hot-Line Live Working Manipulator

2014 ◽  
Vol 610 ◽  
pp. 28-34 ◽  
Author(s):  
Xiao Lin Ma ◽  
Hui Chai ◽  
Yun Jiang Li
Keyword(s):  
Analytical Solutions ◽  
Inverse Kinematics ◽  
Transformation Method ◽  
Forward Kinematics ◽  
Euler Angles ◽  
Kinematics Analysis ◽  
Hydraulic Actuator ◽  
End Effector

This paper introduces the development of hot-line live working manipulators and gives a new configuration manipulator driven by hydraulic actuator firstly. Then, its forward kinematics equations are derived with homogenous transformation method. Finally, the analytical solutions of its inverse kinematics are solved under the condition that the posture of the end-effector is known and given with z-y-z Euler angles.

Design and Analysis of a Biomimetic Wire-Driven Robot Arm

2011 ◽  
Author(s):  
Zheng Li ◽  
Ruxu Du ◽  
Man Cheong Lei ◽  
Song Mei Yuan
Keyword(s):  
Inverse Kinematics ◽  
Geometric Analysis ◽  
Forward Kinematics ◽  
Positioning Error ◽  
Robot Arm ◽  
End Effector ◽  
Fixed Node

Inspired by the octopus and snakes, we designed and built a wire-driven serpentine robot arm. The robot arm is made of a number of rigid nodes connected by two sets of wires. The rigid nodes act as the backbone while the wires work as the muscle, which enables the 2 DOF bending. The forward kinematics is derived using D-H method, while the inverse kinematics and its workspace can be solved by geometric analysis. To validate the design, a prototype is built. It is found that the positioning error of the robot arm is generally less than 2%. The advantage of this robot arm is that with several nodes fixed the rest nodes are still controllable. The positioning error is smaller when the fixed node is closer to the end effector.

Kinematic and Kinetostatic Analysis of Parallel Manipulators with Emphasis on Position, Motion, and Actuation Singularities

Robotica ◽  
2018 ◽  
Vol 37 (4) ◽  
pp. 599-625 ◽  
Author(s):  
M. Kemal Ozgoren
Keyword(s):  
Inverse Kinematics ◽  
Parallel Manipulators ◽  
Singularity Analysis ◽  
The Other ◽  
Forward Kinematics ◽  
Velocity Mapping ◽  
Active Joint ◽  
End Effector ◽  
Jacobian Matrices ◽  
Other Hand

SummaryThis paper provides a contribution to the singularity analysis of the parallel manipulators by introducing the position singularities in addition to the motion and actuation singularities. The motion singularities are associated with the linear velocity mapping between the task and joint spaces. So, they are the singularities of the relevant Jacobian matrices. On the other hand, the position singularities are associated with the nonlinear position mapping between the task and joint spaces. So, they are encountered in the position-level solutions of the forward and inverse kinematics problems. In other words, they come out irrespective of the velocity mapping and the Jacobian matrices. Considering these distinctions, a kinematic singularity is denoted here by one of the four acronyms, which are PSFK (position singularity of forward kinematics), PSIK (position singularity of inverse kinematics), MSFK (motion singularity of forward kinematics), and MSIK (motion singularity of inverse kinematics). There may also occur an actuation singularity (ACTS) concerning the kinetostatic relationships that involve forces and moments. However, it is verified that an ACTS is the same as an MSFK. Each singularity induces different consequences in the joint and task spaces. A PSFK imposes a constraint on the active joint variables and makes the end-effector position indefinite and uncontrollable. Therefore, it must be avoided. An MSFK imposes a constraint on the rates of the active joint variables and makes the end-effector motion indefinite and easily perturbable. Besides, since it is also an ACTS, it causes the actuator torques or forces to grow without bound. Therefore, it must also be avoided. On the other hand, a PSIK imposes a constraint on the end-effector position but provides freedom for the active joint variables. Similarly, an MSIK imposes a constraint on the end-effector motion but provides freedom for the rates of the active joint variables. A PSIK or MSIK need not be avoided if the constraint it imposes on the position or motion of the end-effector is acceptable or if the task can be planned to be compatible with that constraint. Besides, with such a compatible task, a PSIK or MSIK may even be advantageous, because the freedom it provides for the active joint variables can sometimes be used for a secondary purpose. This paper is also concerned with the multiplicities of forward kinematics in the assembly modes of the manipulator and the multiplicities of inverse kinematics in the posture modes of the legs. It is shown that the assembly mode changing poses of the manipulator are the same as the MSFK poses, and the posture mode changing poses of the legs are the same as the MSIK poses.

Three-Dimensional Kinematic Analysis of a Two Actuated Spoke Wheel Robot Based on Its Equivalency to a Serial Manipulator

2008 ◽  
Author(s):  
Ping Ren ◽  
Ya Wang ◽  
Dennis Hong
Keyword(s):  
Inverse Kinematics ◽  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Forward Kinematics ◽  
Future Research ◽  
Ground Contact ◽  
Contact Points ◽  
Prismatic Joints ◽  
Forward Kinematic ◽  
The Relationship

In this paper, the inverse and forward kinematics of a novel mobile robot that utilizes two actuated spoke wheels is presented. Intelligent Mobility Platform with Active Spoke System (IMPASS) is a wheel-leg hybrid robot that can walk in unstructured environments by stretching in or out three independently actuated spokes of each wheel. First, the unique locomotion scheme of IMPASS is introduced. Then the configuration of the robot when each of its two spoke wheels has one spoke in contact with the ground is modeled as a two-branch parallel mechanism with spherical and prismatic joints. An equivalent serial manipulator of the 2-SP mechanism with the same degrees of freedom is proposed to solve for the inverse and forward kinematic problems. The relationship between the physical limits of the stroke of the spokes (effective spoke length) and the limits of its equivalent degree of freedom is established. This approach can also be expanded to deal with the forward and inverse kinematics of other configurations which has more than two ground contact points. Several examples are used to illustrate the method. The results obtained will be used in the future research on the motion planning of IMPASS walking in unstructured environment.

scholarly journals Computational Analysis of Kinematics of 3 – Links Articulated Robotic Manipulator

2019 ◽  
Vol 9 (2) ◽  
pp. 3640-3643
Keyword(s):  
Inverse Kinematics ◽  
Computational Analysis ◽  
Robot Manipulators ◽  
Robotic Manipulator ◽  
Robotic Arm ◽  
Forward Kinematics ◽  
End Effector ◽  
Computational Estimation ◽  
Arm Motion ◽  
Free Body

The Computational Analysis of Kinematics of 3 – Links Articulated Robotic Manipulator has been presented in this. The design of robot manipulators requires accurate computational analysis, involving the geometric position of the linking arms. The method of Forward Kinematics and Inverse Kinematics were employed in estimating the robotic arm’s position with respect to link lengths and angle, in which the angle required to move the end effector to a desired position is estimated and determined. A three link robotic arm with a rigid rotational base was also illustrated using free body diagrams, and computational estimation of the required parameters. The outcomes of the forward kinematics reveals that the robot end effector position can be estimated using the values of x, y, and z coordinates thereby providing a better means of controlling or adapting robot’s arm/motion to its environment.

Digital Human Forward Kinematic and Dynamic Reliabilities

2013 ◽  
Vol 135 (7) ◽  
Author(s):  
Jared Gragg ◽  
James Yang
Keyword(s):  
Inverse Kinematics ◽  
Probabilistic Approach ◽  
Probabilistic Methods ◽  
Probabilistic Design ◽  
Digital Human Modeling ◽  
End Effector ◽  
Dynamic Reliability ◽  
Human Modeling ◽  
Forward Kinematic ◽  
Digital Human

Probabilistic methods have been applied to many problems in various fields of study. There are many distinct applications of probabilistic design in the biomechanics field, in particular. Traditionally, deterministic methods have been applied in digital human modeling (DHM). Transforming the deterministic approach of digital human modeling into a probabilistic approach is natural since there is inherent uncertainty and variability associated with DHM problems. Typically, deterministic studies in this field ignore this uncertainty or try to limit the uncertainty by employing optimization procedures. Often, inverse kinematics or dynamics techniques are introduced to point the system to the desired solution, or “best solution.” Due to the variability in the inputs, a deterministic study may not be enough to account for the uncertainty in the system. Probabilistic design techniques allow the designer to predict the likelihood of an outcome while also accounting for uncertainty, in contrast to deterministic studies. The purpose of this study is to incorporate probabilistic approaches to a deterministic DHM problem that has already been studied, analyzing human forward kinematics and dynamics. The problem is transformed into a probabilistic approach where the human forward kinematic and dynamic reliabilities are determined. The forward kinematic reliability refers to the probability that the human end-effector position (and/or orientation) falls within a specified distance from the desired position (and/or orientation) in an inverse kinematics problem. The forward dynamic reliability refers to the probability that the human end-effector position (and/or velocity) falls within a specified distance from the desired position (and/or velocity) along a specified trajectory in the workspace. The dynamic equations of motion are derived by the Lagrangian backward recursive dynamics formulation.

Kinematics of a planar slider-crank linkage in screw form

2021 ◽  
pp. 095440622110207
Author(s):  
Jing-Shan Zhao ◽  
Songtao Wei ◽  
Junjie Ji
Keyword(s):  
Angular Velocity ◽  
Inverse Kinematics ◽  
Parallel Mechanism ◽  
Numerical Algorithms ◽  
Forward Kinematics ◽  
End Effector ◽  
First Order ◽  
Forward And Inverse Kinematics ◽  
Definition Of ◽  
Inverse Velocity

This paper investigates the forward and inverse kinematics in screw coordinates for a planar slider-crank linkage. According to the definition of a screw, both the angular velocity of a rigid body and the linear velocity of a point on it are expressed in screw components. Through numerical integration on the velocity solution, we get the displacement. Through numerical differential interpolation of velocity, we gain the acceleration of any joint. Traditionally, position and angular parameters are usually the only variables for establishing the displacement equations of a mechanism. For a series mechanism, the forward kinematics can be expressed explicitly in the variable of position parameters while the inverse kinematics will have to resort to numerical algorithms because of the multiplicity of solution. For a parallel mechanism, the inverse kinematics can be expressed explicitly in the variable of position parameters of the end effector while the forward kinematics will have to resort to numerical algorithms because of the nonlinearity of system. Therefore this will surely lead to second order numerical differential interpolation for the calculation of accelerations. The most prominent merit of this kinematic algorithm is that we only need the first order numerical differential interpolation for computing the acceleration. To calculate the displacement, we also only need the first order numerical integral of the velocity. This benefit stems from the screw the coordinates of which are velocity components. The example of planar four-bar and five-bar slider-crank linkages validate this algorithm. It is especially suited to developing numerical algorithms for forward and inverse velocity, displacement and acceleration of a linkage.

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