scholarly journals A Tabular Format for Computing Inverse Kinematic Equations for a 3DOF Robot Leg

10.5772/7234 ◽  
2009 ◽  
Vol 6 (3) ◽  
pp. 26 ◽  
Author(s):  
F. Nickols
Keyword(s):  
Power Series ◽  
High Speed ◽  
Degrees Of Freedom ◽  
Inverse Kinematic ◽  
Coordinate Space ◽  
Power Series Method ◽  
Cylindrical Coordinate ◽  
Field Programmable ◽  
Robot Leg ◽  
Three Degrees Of Freedom

A method is presented for accurately computing the three servomechanism angles that place the leg tip of a 3DOF robot leg in cylindrical coordinate space, R, θ, Z. The method is characterized by (i) a multivariable integer power series for each degree of freedom that can be used to replace traditional trigonometrical functions, and, (ii) only integer numbers are used. A technique is shown that derives the coefficients, Ci j k, of each of the terms in the series that represents a servomechanism angle, S. This power series method has the advantage of; (i) satisfying accuracy requirements, (ii) producing a unique solution, (iii) high speed realtime computation, (iv) low memory requirement and (v) implementation into a generic algorithm or hardware such as a field programmable gate array. The series can represent many continuous kinematic systems just by changing the values of the coefficients. The coefficients are rapidly computed via a spreadsheet. The method can be extended to more than three degrees of freedom and also mapped into other coordinate frames such as a Cartesian or spherical.

Kinematics Optimization of a 3-SPS Parallel Redundant Motion Mechanism Using Conformal Geometric Algebra

2015 ◽  
Vol 789-790 ◽  
pp. 889-895
Author(s):  
Jahng Hyon Park ◽  
Jeseok Kim ◽  
Jin Han Jeong
Keyword(s):  
High Speed ◽  
Degrees Of Freedom ◽  
Optimization Technique ◽  
Optimal Solution ◽  
Inverse Kinematic ◽  
Fast Reaction ◽  
Inverse Kinematic Problem ◽  
Time Optimal ◽  
Parallel Link ◽  
Spherical Parallel Manipulator

In this paper, an actuation mechanism for high-speed aiming of a target is proposed. The mechanism is a 3DOF-SPS (spherical-prismatic-spherical) parallel manipulator and can be used for a missile defense system with a fast reaction time. This type of parallel mechanism has high rigidity against external disturbances and accordingly high stiffness and precision. The target aiming requires 2 degrees of freedom and this 3 DOF mechanism has one redundancy. For fast manipulation of the proposed mechanism, the redundancy can be exploited and an optimal solution can be found out of the infinite number of inverse kinematic solutions. For finding a near time-optimal solution, a cost function is formulated considering displacement of each parallel link and an optimization technique is used for solution of the inverse kinematic problem.

scholarly journals Trajectory planning of multiple coordinating robots using genetic algorithms

Robotica ◽  
1996 ◽  
Vol 14 (2) ◽  
pp. 227-234 ◽  
Author(s):  
Shudong Sun ◽  
A.S. Morris ◽  
A.M.S. Zalzala
Keyword(s):  
Genetic Algorithms ◽  
Trajectory Planning ◽  
Degrees Of Freedom ◽  
Coordinate Space ◽  
Object A ◽  
Dynamic Constraints ◽  
Order Polynomial ◽  
Cartesian Coordinate ◽  
Three Degrees Of Freedom

SUMMARYThe paper focuses on the problem of trajectory planning of multiple coordinating robots. When multiple robots collaborate to manipulate one object, a redundant system is formed. There are a number of trajectories that the system can follow. These can be described in Cartesian coordinate space by an nth order polynomial. This paper presents an optimisation method based on the Genetic Algorithms (GAs) which chooses the parameters of the polynomial, such that the execution time and the drive torques for the robot joints are minimized. With the robot's dynamic constraints taken into account, the pitimised trajectories are realisable. A case study with two planar-moving robots, each having three degrees of freedom, shows that the method is effective.

scholarly journals A Translational Three-Degrees-of-Freedom Parallel Mechanism With Partial Motion Decoupling and Analytic Direct Kinematics

2020 ◽  
Vol 12 (2) ◽  
Author(s):  
Huiping Shen ◽  
Damien Chablat ◽  
Boxiong Zeng ◽  
Ju Li ◽  
Guanglei Wu ◽  
...  
Keyword(s):  
Parallel Mechanism ◽  
Design Theory ◽  
Degrees Of Freedom ◽  
Analytic Solutions ◽  
Inverse Kinematic ◽  
Kinematic Modeling ◽  
Topological Design ◽  
Prismatic Joints ◽  
Topological Characteristics ◽  
Three Degrees Of Freedom

Abstract According to the topological design theory and the method of parallel mechanism (PM) based on position and orientation characteristic (POC) equations, this paper studied a three-degrees-of-freedom (3-DOF) translational PM that has three advantages, i.e., (i) it consists of three fixed actuated prismatic joints, (ii) the PM has analytic solutions to the direct and inverse kinematic problems, and (iii) the PM is of partial motion decoupling property. First, the main topological characteristics, such as the POC, degree-of-freedom, and coupling degree, were calculated for kinematic modeling. Thanks to these properties, the direct and inverse kinematic problems can be readily solved. Further, the conditions of the singular configurations of the PM were analyzed, which corresponds to its partial motion decoupling property.

scholarly journals Kinematic Analysis and Trajectory Planning of the Orthoglide 5-Axis

2015 ◽  
Author(s):  
S. Caro ◽  
D. Chablat ◽  
P. Lemoine ◽  
P. Wenger
Keyword(s):  
Trajectory Planning ◽  
Kinematic Analysis ◽  
High Speed ◽  
Degrees Of Freedom ◽  
Kinematic Model ◽  
Inverse Kinematic ◽  
Hybrid Architecture ◽  
Parallel Kinematic Machine ◽  
Control Loop ◽  
Parallel Kinematic

The subject of this paper is about the kinematic analysis and the trajectory planning of the Orthoglide 5-axis. The Orthoglide 5-axis a five degrees of freedom parallel kinematic machine developed at IRCCyN and is made up of a hybrid architecture, namely, a three degrees of freedom translational parallel manipulator mounted in series with a two degrees of freedom parallel spherical wrist. The simpler the kinematic modeling of the Orthoglide 5-axis, the higher the maximum frequency of its control loop. Indeed, the control loop of a parallel kinematic machine should be computed with a high frequency, i.e., higher than 1.5 MHz, in order the manipulator to be able to reach high speed motions with a good accuracy. Accordingly, the direct and inverse kinematic models of the Orthoglide 5-axis, its inverse kinematic Jacobian matrix and the first derivative of the latter with respect to time are expressed in this paper. It appears that the kinematic model of the manipulator under study can be written in a quadratic form due to the hybrid architecture of the Orthoglide 5-axis. As illustrative examples, the profiles of the actuated joint angles (lengths), velocities and accelerations that are used in the control loop of the robot are traced for two test trajectories.

Multibody Analysis and Design of a Reconfigurable Parallel Kinematics Manipulator

2015 ◽  
Author(s):  
Matteo Palpacelli ◽  
Massimo Callegari ◽  
Luca Carbonari ◽  
Giacomo Palmieri
Keyword(s):  
Control Strategy ◽  
Degrees Of Freedom ◽  
Parallel Kinematics ◽  
Analysis And Design ◽  
Pure Rotation ◽  
Analytic Expressions ◽  
Robot Leg ◽  
Moving Platform ◽  
Actuation Systems ◽  
Three Degrees Of Freedom

This paper presents the design of a reconfigurable parallel kinematics machine endowed with three degrees of freedom of pure translation, or alternately of pure rotation. Such reconfigurability results from the use of lockable spherical joints, which realize the connection between each robot leg and the moving platform. Three actuated legs are used to drive the platform motion. The change of configuration occurs only at a specific pose, called home configuration. A control strategy allows to manage the shift phase and activate the two mobilities one at a time. Multibody simulations allowed to analyze the dynamic behavior of the manipulator and to verify the choices made with regard to the robot mechanics and the size of actuation systems. Position and differential kinematics of the manipulator are briefly introduced in order to demonstrate the simplicity of the analytic expressions and the mechanical feasibility of the manipulator.

scholarly journals Technology-Oriented Optimization of the Secondary Design Parameters of Robots for High-Speed Machining Applications

2010 ◽  
Author(s):  
Se´bastien Briot ◽  
Anatol Pashkevich ◽  
Damien Chablat
Keyword(s):  
Machine Tools ◽  
High Speed ◽  
Degrees Of Freedom ◽  
Parallel Robots ◽  
Design Parameters ◽  
Speed Up ◽  
Parallel Kinematic ◽  
Parallel Kinematic Machine Tools ◽  
Accuracy Constraints ◽  
Three Degrees Of Freedom

In this paper, a new methodology for the optimal design of the secondary geometric parameters (shape of links, size of the platform, etc.) of parallel kinematic machine tools is proposed. This approach aims at minimizing the total mass of the robot under position accuracy constraints. This methodology is applied to two translational parallel robots with three degrees-of-freedom (DOF): the Y-STAR and the UraneSX. The proposed approach is able to speed up the design process and to help the designer to find more quickly a set of design parameters.

scholarly journals Kinematic Analysis of a Parallel-Sequential Structure Mechanism with Five Degrees of Freedom

2019 ◽  
pp. 18-24
Author(s):  
G.S. Filippov
Keyword(s):  
Numerical Experiment ◽  
Kinematic Analysis ◽  
Degrees Of Freedom ◽  
Inverse Kinematic ◽  
Parallel Structure ◽  
Kinematic Pair ◽  
Inverse Kinematic Problem ◽  
Sequential Structure ◽  
Spine Movement ◽  
Three Degrees Of Freedom

The article presents a synthesis of a mechanism of parallel-sequential structure with five degrees of freedom capable of processing objects with an extended dimention in one direction, wherein the considered mechanism can have a high bearing capacity. Corresponding problems are associated with manufacturing jet turbine airfoil as well as vertebrae operations (on the human spine). Movement along a coordinate that is linked to large dimensions of a processed object is provided using the initial translation pairs equipped with a motor. It is followed by a flat partial parallel structure mechanism with three degrees of freedom, and further – by a revolute kinematic pair. A kinematic analysis of the considered mechanism is performed, and the inverse kinematic problem is solved. The Angeles-Gosselin method for parallel structure mechanisms is used when performing velocity calculations of the parallel-sequential structure mechanism. The results of the numerical experiment are presented.

Research on Hydraulic and Control System of Manipulator

2012 ◽  
Vol 482-484 ◽  
pp. 1350-1353
Author(s):  
Ji Li He
Keyword(s):  
Degrees Of Freedom ◽  
Hydraulic Cylinder ◽  
Simulation Software ◽  
Simulation Function ◽  
Hydraulic Circuit ◽  
Hydraulic Simulation ◽  
Industrial Manipulator ◽  
Cylindrical Coordinate ◽  
And Control ◽  
Three Degrees Of Freedom

The industrial manipulator has been introduced. The manipulator of cylindrical coordinate type provides with three degrees of freedom including rotation, lifting and expansion, which has corresponding rotation structure, lifting structure, expansion structure. All parts are drove and controlled by using hydraulic cylinder. FluidSIM-H is hydraulic simulation software and tightly integrated the CAD function and simulation function. To simulate and analyze the operation of hydraulic circuit which based on the physical model of hydraulic element and LOGO control. The results showed that the industrial manipulator can work reliably.

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