Displacement Analysis of a Spatial 7R Mechanism—A Generalized Lobster’s Arm

1979 ◽  
Vol 101 (2) ◽  
pp. 224-231 ◽  
Author(s):  
J. Duffy ◽  
S. Derby
Keyword(s):  
Mathematical Model ◽  
Kinematic Analysis ◽  
Input Output ◽  
Major Step ◽  
Displacement Analysis ◽  
The Mathematical Model ◽  
Output Equation

An input-output equation of degree 24 is derived for a spatial 7R mechanism with consecutive pair axes intersecting. This mechanism is essentially the mathematical model for the kinematic analysis of a lobster’s arm which is an open 6R chain with mutually perpendicular consecutive pair axes, the geometry of which was first described by Willis [4] in 1841. The analysis of this special 7R mechanism constitutes a major step towards the solution of the general 7R mechanism with seven axes arbitrarily oriented in space.

Kinematic Analysis of Spatial Six-Link 3R-2P-C Mechanisms

1976 ◽  
Vol 4 (2) ◽  
pp. 71-76
Author(s):  
M.O.M. Osman ◽  
R. V. Dukkipati
Keyword(s):  
Closed Form ◽  
Kinematic Analysis ◽  
Input Output ◽  
Variable Parameters ◽  
Output Displacement ◽  
Loop Equation ◽  
Dual Number ◽  
Input And Output ◽  
Order Polynomial ◽  
Output Equation

Using (3 x 3) matrices with dual-number elements, closed-form displacement relationships are derived for a spatial six-link R-C-P-R-P-R mechanism. The input-output closed form displacement relationship is obtained as a second order polynomial in the output displacement. For each set of the input and output displacements obtained from the equation, all other variable parameters of the mechanism are uniquely determined. A numerical illustrative example is presented. Using the dual-matrix loop equation, with proper arrangement of terms and following a procedure similar to that presented, the closed-form displacement relationships for other types of six-link 3R + 2P + 1C mechanisms can be obtained. The input-output equation derived may also be used to generate the input-output functions for five-link 2R + 2C + 1P mechanisms and four-link mechanisms with one revolute and three cylinder pairs.

Displacement Analysis of a Special Case of the 7R, Single-Loop, Spatial Mechanism

1983 ◽  
Vol 105 (1) ◽  
pp. 78-87
Author(s):  
Hiram Albala ◽  
David Pessen
Keyword(s):  
Input Output ◽  
Fourth Degree ◽  
Displacement Analysis ◽  
Single Loop ◽  
Spatial Mechanism ◽  
Rotation Axes ◽  
Successive Rotation ◽  
Special Case ◽  
Output Equation

Based on the displacement equations for the general n-bar, single-loop spatial linkage, obtained elsewhere, the displacement analysis for a special case of the 7R spatial mechanism is carried out. In this mechanism the successive rotation axes are perpendicular to each other, the distances between axes 3-4, 4-5, 5-6, are equal and the offsets along axes 4 and 5 are zero, when input axis is labeled axis 1. In this fashion, there still remain nine free linkage parameters. Input-output equation is of the eighth-degree in the tangent of half the output angle. A particular case of this one, where all the distances between axes are equal and all the offsets along axes are zero, leads to an input-output equation of the fourth-degree in the same quantity, with a maximum of four closures. This mechanism resulted to be a double-rocker.

General Characteristics of the Motion of Multiple-Pode Joints

1984 ◽  
Vol 51 (1) ◽  
pp. 171-178 ◽  
Author(s):  
T. W. Lee ◽  
E. Akbil
Keyword(s):  
Functional Analysis ◽  
Analytical Method ◽  
Input Output ◽  
Displacement Analysis ◽  
General Displacement ◽  
Motion Parameters ◽  
The Creation ◽  
Motion Characteristics ◽  
And Behavior ◽  
Output Equation

This paper presents an analytical method on the investigation of the motion characteristics of a class of spatial mechanical components involving the ball-and-trunnion type of joint, namely, the multiple-pode joint. Algebraic derivations of the input-output equation and explicit relations for motion parameters are presented for these joints as well as their shaft couplings. From this general displacement analysis, some insights into the basic nature and behavior of the multiple-pode joint are observed and interpreted. The creation of shaft couplings using these joints and their functional analysis are also illustrated in several cases.

Kinematic Analysis of 5-UPS Parallel Machine Tool Based on Adams

2014 ◽  
Vol 644-650 ◽  
pp. 215-219 ◽  
Author(s):  
Lin Cai
Keyword(s):  
Mathematical Model ◽  
Machine Tool ◽  
Kinematic Analysis ◽  
Inverse Kinematics ◽  
Parallel Machine ◽  
Inverse Solution ◽  
Robot Kinematics ◽  
Vector Method ◽  
Parallel Machine Tool ◽  
The Mathematical Model

In this paper, the kinematics of 5-UPS parallel machine tool is analyzed, and a kinematic analysis method combining kinematic analysis and computer kinematics software is proposed. Under the premise that the parallel machine tool sector parameters is known, firstly we use the vector method to establish a mathematical model of inverse kinematics, and in accordance with a U-shaped processing trajectory the inverse solution is calculated; Secondly, three-dimensional model of the parallel machine tool is modeled in Adams, and kinematic constraints are set correctly; Finally, the inverse kinematics solution of the mathematical model is used as the Adams drive input, then the positive solutions is carried out. Compared through the Adams simulation results with U-machining path, it is verified that the inverse solution of the mathematical model and parallel machine tool bodies both are correct, it has certain significance for Parallel machine tools and other parallel robot kinematics analysis.

Forward displacement analysis of a 3-RPR spherical parallel mechanism

2013 ◽  
Vol 227 (8) ◽  
pp. 1864-1869 ◽  
Author(s):  
Duanling Li ◽  
Zhonghai Zhang ◽  
He Li
Keyword(s):  
Mathematical Model ◽  
Parallel Mechanism ◽  
Spherical Geometry ◽  
Parallel Mechanisms ◽  
Forward Displacement ◽  
Displacement Analysis ◽  
Spherical Parallel Mechanism ◽  
The Mathematical Model ◽  
Forward Displacement Analysis ◽  
Modeling Equation

The forward displacement analysis of spherical parallel mechanisms is a nonlinear problem and has attracted the attention of many researchers. A method is proposed to analyze the forward displacement of a 3-RPR spherical parallel mechanism. Firstly, based on spherical geometry and spherical trigonometry theory, a mathematical model is derived for the forward displacement analysis of the spherical parallel mechanism. After simplifying the mathematical model, the kinematical equations are then solved using the resultant elimination method. Using this method, one can obtain the three variables representing the position and pose of the moving platform directly. Finally, a numerical example is presented and Autodesk Inventor software is used to verify all the real solutions. The method of mathematical modeling, equation simplification, resultant elimination presented in this paper can be extended to solve similar problems effectively.

scholarly journals A New Model-Free Predictive Control Method Using Input and Output Data

2014 ◽  
Vol 1042 ◽  
pp. 182-187 ◽  
Author(s):  
Shigeru Yamamoto
Keyword(s):  
Mathematical Model ◽  
Predictive Control ◽  
Control Method ◽  
Just In Time ◽  
Control Input ◽  
Input Output ◽  
Output Data ◽  
Online Data ◽  
Model Free ◽  
The Mathematical Model

The purpose of this paper is to present a new predictive control utilizing online data and stored data of input/output of the controlled system. The conventional predictive control methods utilize the mathematical model of the control system to predict an optimal future input to control the system. The model is usually obtained by a standard system identification method from the measured input/output data. The proposed method does not require the mathematical model to predict the optimal future control input to achieve the desired output. This control strategy, called just-in-time, was originally proposed by Inoue and Yamamoto in 2004. In this paper, we proposed a simplified version of the original just-in-time predictive control method.

scholarly journals COMPUTER SIMULATION AND ANALYTICAL SOLUTION OF FOUR BAR MECHANISM

2020 ◽  
pp. 120-128
Author(s):  
Darina Hroncová
Keyword(s):  
Mathematical Model ◽  
Analytical Solution ◽  
Mathematical Models ◽  
Computer Model ◽  
Analytical Methods ◽  
Kinematic Analysis ◽  
Linkage Mechanism ◽  
The Creation ◽  
Four Bar Linkage ◽  
The Mathematical Model

Urgency of the research. The use of computers in technical practice leads to the extension of the possibility of solving mathematical models. This makes it possible to gradually automate complex calculations of equations of mathematical models. It is necessary to input the relevant inputs of the mathematical model, to build a simulation computer model and to monitor and evaluate the output results using a computer's output device. Target setting. The possibilities of modeling a four-bar linkage mechanism by classical analytical methods and methodsusing computer modeling are presented in this paper.The problem is to describe the creation of a computer model and to show the mathematical model and its solution in the classical ways. Actual scientific researches and issues analysis. The inspiration for the creation of the article was the study of the mechanisms in the work [1-3] and the study of other resources available in library and journal materials, as well as prepared study materials for students of Technical university Kosice. Uninvestigated parts of general matters defining. The question of building a real mechanism model. The possibilities to building a real model, based on the result of simulation. The research objective. The aim of this paper is to develop a functional model of the mechanism in ADAMS/View and Matlab and its complete kinematic analysis.The statement of basic materials.The task was to create a computer model in MSC Adams and Matlab and to perform a four-bar linkage mechanism kinematic analysis. At the same time the classical procedure of analytical methods of kinematic analysis was described. Kinematic сharacteristics of driven members and their selected points were determined. The movement of the parts of the mechanism in its significant points was analyzed. The results of the solution were shown in both programs in graphical form. Kinematic analysis was performed by both vector and graphical methods. Finally, the results with a graphical representation of parameters such as angular displacement, angular velocity and angular acceleration of mechanism members are presented in this work. The results of these solutions are created in the form of graphs. To ensure that the results do not differ from the model real, a good computer model gradually was created by its verification and modification, which is one of the advantages of MSC Adams. The practical applicability of the mathematical model was limited by the existence of an analytical solution. Conclusions. The development of computer technology has expanded the limit of solvability of mathematical models and made it possible to gradually automate the calculation of equations of mathematical models. In a computer model the auto-mated calculation can be treated as a real object sample. In various variations of calculation, we can monitor and measure the behavior of an object under different conditions, under the influence of different inputs. Graphical and vector methods were used for classical analytical methods. MSC Adams and Matlab were used for the automated calculations.

scholarly journals Kinematic analysis of Felix Baumgartner's stratospheric jump in 2012

2021 ◽  
Vol 10 (3) ◽  
Author(s):  
Josemaria Zavala ◽  
Jimmy Menendez
Keyword(s):  
Mathematical Model ◽  
Kinematic Analysis ◽  
Action Plan ◽  
Velocity Model ◽  
Scientific Achievement ◽  
Mathematical Exploration ◽  
Scientific Report ◽  
The Mathematical Model ◽  
Red Bull

The present investigation shows a kinematic analysis of Baumgartner’s stratospheric jump, based on a scientific report by Red Bull. The modeling was carried out using the different forces that intervened in the event (velocity, acceleration, etc.), making it possible to generate a mathematical model capable of extrapolating data and allowing us a better appreciation of such scientific achievement. All the mathematical exploration has been carried out with ten decimal places; however, they will be rounded to four in writing. The action plan was based on obtaining the velocities by placing points on a velocity model belonging to an approximate graph of a Red Bull scientific report, which was put into the GeoGebra Classic 5 program to find the velocities. After this, we proceeded to find the accelerations and the formula of the function that models them. Finally, this formula was integrated to acquire the mathematical model of the velocities. 

Kinematic and Stiffness Analysis of an Origami-Type Carton

2013 ◽  
Author(s):  
C. Qiu ◽  
Vahid Aminzadeh ◽  
Jian S. Dai
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Angular Velocity ◽  
Kinematic Analysis ◽  
Stiffness Analysis ◽  
Revolute Joints ◽  
Stiffness Characteristics ◽  
The Individual ◽  
The Mathematical Model ◽  
Equivalent Mechanism

This paper investigates the stiffness characteristics of an origami-type carton, which can be modeled into an equivalent mechanism by considering creases as revolute joints and panels as links. Stiffness characteristics of a single crease is investigated regarding its relationships with folding angular velocity and crease length. Based on the kinematic analysis of carton folding, the aggregated stiffness is obtained by integrating the individual crease stiffness into the equivalent mechanism. Finally experiment results of carton folding manipulation are obtained, and comparisons between the mathematical model and experimental data show that the model predicts the carton’s behaviour well.

Displacement Analysis of Spatial Six-Link, 5R-C Mechanisms: A General Solution

1985 ◽  
Vol 107 (3) ◽  
pp. 353-357 ◽  
Author(s):  
Xu Li Ju ◽  
J. Duffy
Keyword(s):  
General Solution ◽  
Angular Displacement ◽  
Problem Formulation ◽  
Input Output ◽  
Displacement Analysis ◽  
Numerical Example ◽  
Single Operation ◽  
Half Angle ◽  
Output Equation

Four angular displacement equations are derived for the spatial 5R-C hexagon from which an input-output equation of 16th degree in the tan-half-angle of the output angular displacement for each of the RCRRRR, RRCRRR mechanisms and the yet unsolved RRRRRC2 mechanism can be obtained by the elimination of two unwanted variables in a single operation. This novel problem formulation is a general solution for all 5R-C mechanisms. Results are verified by a numerical example.

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