Inverse Kinematics with 3-Dimensational Tool Compensation for 5-Axis Machine Center of Tilting Rotary Table

2011 ◽  
Vol 110-116 ◽  
pp. 3525-3533
Author(s):  
Chieh Tung ◽  
Pei Lum Tso
Keyword(s):  
Closed Form ◽  
Inverse Kinematics ◽  
Compensation Method ◽  
Spindle Orientation ◽  
Rotary Table ◽  
Machine Center ◽  
Radius Compensation ◽  
Tool Compensation ◽  
Milling Tools

The purpose of this paper is to develop a tool radius compensation method for a 5-axis horizontal machine center with a tilting rotary table. The generalized expression is presented first to determine the cutting contact location for any type of milling tools. The spindle orientation solved from a closed form of the inverse kinematics is applied for generating the postprocessor, and a compensating procedure is implemented to verify the offset path.

scholarly journals IKBT: Solving Symbolic Inverse Kinematics with Behavior Tree (Extended Abstract)

2020 ◽  
Author(s):  
Dianmu Zhang ◽  
Blake Hannaford
Keyword(s):  
Closed Form ◽  
Inverse Kinematics ◽  
Intelligent System ◽  
Logical Reasoning ◽  
Robot Arm ◽  
Kinematics Analysis ◽  
Closed Form Solutions ◽  
Behavior Tree ◽  
Behavior Trees ◽  
High Level

Inverse kinematics solves the problem of how to control robot arm joints to achieve desired end effector positions, which is critical to any robot arm design and implementations of control algorithms. It is a common misunderstanding that closed-form inverse kinematics analysis is solved. Popular software and algorithms, such as gradient descent or any multi-variant equations solving algorithm, claims solving inverse kinematics but only on the numerical level. While the numerical inverse kinematics solutions are relatively straightforward to obtain, these methods often fail, even when the inverse kinematics solutions exist. Therefore, closed-form inverse kinematics analysis is superior, but there is no generalized automated algorithm. Up till now, the high-level logical reasoning involved in solving closed-form inverse kinematics made it hard to automate, so it's handled by human experts. We developed IKBT, a knowledge-based intelligent system that can mimic human experts' behaviors in solving closed-from inverse kinematics using Behavior Tree. Knowledge and rules used by engineers when solving closed-from inverse kinematics are encoded as actions in Behavior Tree. The order of applying these rules is governed by higher level composite nodes, which resembles the logical reasoning process of engineers. It is also the first time that the dependency of joint variables, an important issue in inverse kinematics analysis, is automatically tracked in graph form. Besides generating closed-form solutions, IKBT also explains its solving strategies in human (engineers) interpretable form. This is a proof-of-concept of using Behavior Trees to solve high-cognitive problems.

Kinematics of a n–bay triangle–triangle variable geometry truss manipulator

Robotica ◽  
1992 ◽  
Vol 10 (3) ◽  
pp. 263-267
Author(s):  
L. Beiner
Keyword(s):  
Iterative Method ◽  
Closed Form ◽  
Inverse Kinematics ◽  
Variable Length ◽  
Variable Geometry ◽  
Closed Form Solutions ◽  
Numerical Example ◽  
Forward And Inverse Kinematics ◽  
Variable Geometry Truss Manipulator ◽  
Variable Geometry Truss

SUMMARYVariable geometry truss manipulators (VGTM) are static trusses where the lengths of some members can be varied, allowing one to control the position of the free end relative to the fixed one. This paper deals with a planar VGTM consisting of a n–bay triangle-triangle truss with one variable length link (i.e. one DOF) per bay. Closed-form solutions to the forward, inverse, and velocity kinematics of a 3-DOF version of this VGTM are presented, while the forward and inverse kinematics of an n–DOF (redundant) one are solved by a recursive and an iterative method, respectively. A numerical example is presented.

Generation of closed-form inverse kinematics for reconfigurable robots

2008 ◽  
Vol 3 (1) ◽  
pp. 91-96 ◽  
Author(s):  
Jie Zhao ◽  
Weizhong Wang ◽  
Yongsheng Gao ◽  
Hegao Cai
Keyword(s):  
Closed Form ◽  
Inverse Kinematics ◽  
Reconfigurable Robots

Automated inverse-kinematics for robot off-line programming

Robotica ◽  
1994 ◽  
Vol 12 (1) ◽  
pp. 45-53 ◽  
Author(s):  
W.Edward Red ◽  
Shao-Wei Gongt
Keyword(s):  
Closed Form ◽  
Inverse Kinematics ◽  
Broad Class ◽  
Inverse Kinematic ◽  
Degree Of Freedom ◽  
Lower Degree ◽  
Serial Robots ◽  
Automated Methods ◽  
Kinematic Solution

Automated methods are developed to classify a robot's kinematic type and select an appropriate library inverse-kinematic solution based on this classification. These methods automatically generate DenavitHartenberg joint frame parameters, given any frame representation that can mathematically be represented as a homogeneous transformation.To reduce the number of closed-form inverse-kinematics solutions required for a broad class of serial robots, additional methods account for differences in robot zero state, base frame location, and joint polarity. Further generalization results from using joint frame decoupling to map lower degree-of-freedom robots into the inverse-kinematics solutions of higher degree-offreedom robots.

scholarly journals Real-Time Inverse Kinematics of the Human Arm

1996 ◽  
Vol 5 (4) ◽  
pp. 393-401 ◽  
Author(s):  
Deepak Tolani ◽  
Norman I. Badler
Keyword(s):  
Closed Form ◽  
Real Time ◽  
Upper Bound ◽  
Multiple Solutions ◽  
Inverse Kinematics ◽  
Additional Constraint ◽  
Degree Of Freedom ◽  
Empirical Results ◽  
Human Arm ◽  
Real Time Applications

A simple inverse kinematics procedure is proposed for a seven degree of freedom model of the human arm. Two schemes are used to provide an additional constraint leading to closed-form analytical equations with an upper bound of two or four solutions, Multiple solutions can be evaluated on the basis of their proximity from the rest angles or the previous configuration of the arm. Empirical results demonstrate that the procedure is well suited for real-time applications.

The Kinematics of Wheeled Mobile Robots With Dual-Wheel Transmission Units

2007 ◽  
Vol 130 (1) ◽  
Author(s):  
Chao Chen ◽  
Svetlana Ostrovskaya ◽  
Jorge Angeles
Keyword(s):  
Mobile Robots ◽  
Closed Form ◽  
Trajectory Tracking ◽  
Inverse Kinematics ◽  
Driving Mechanism ◽  
Ground Contact ◽  
Wheeled Mobile Robots ◽  
Closed Form Solutions ◽  
Novel Technique ◽  
Curve Method

The dual-wheel transmission unit, an innovative driving mechanism for wheeled mobile robots, was introduced elsewhere. In this paper, we discuss wheeled mobile robots with such units, supplied with a novel suspension to keep the wheel-ground contact in spite of the irregularities of the floor. We derive closed-form solutions and constraints pertaining to the direct and inverse-kinematics problems of these robots; the constraints reveal the mobility of the robots at hand. Furthermore, we provide an algorithm for the trajectory tracking of the same robots that relies on a novel technique, which is termed the companion-curve method.

Structure design and kinematics of a robot manipulator

Robotica ◽  
1988 ◽  
Vol 6 (4) ◽  
pp. 299-309 ◽  
Author(s):  
Kesheng Wang ◽  
Terje K. Lien
Keyword(s):  
Numerical Solution ◽  
Closed Form ◽  
Inverse Kinematics ◽  
Degrees Of Freedom ◽  
Robot Manipulator ◽  
Closed Form Solution ◽  
Form Solution ◽  
Structure Design ◽  
General Algorithm ◽  
6 Degrees Of Freedom

SUMMARYIn this paper we show that a robot manipulator with 6 degrees of freedom can be separated into two parts: arm with the first three joints for major positioning and wrist with the last three joints for major orienting. We propose 5 arms and 2 wrists as basic construction for commercially robot manipulators. This kind of simplification can lead to a general algorithm of inverse kinematics for the corresponding configuration of different combinations of arm and wrist. The approaches for numerical solution and closed form solution presented in this paper are very efficient and easy for calculating the inverse kinematics of robot manipulator.

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