Variable Degree-of-Freedom Spatial Mechanisms Composed of Four Circular Translation Joints

2021 ◽  
Author(s):  
Xianwen Kong
Keyword(s):  
Degree Of Freedom ◽  
Variable Degree ◽  
Spatial Mechanisms

Variable Degree-of-Freedom Spatial Mechanisms Composed of Four Circular Translation Joints

2020 ◽  
Author(s):  
Xianwen Kong
Keyword(s):  
Configuration Space ◽  
Screw Theory ◽  
Degree Of Freedom ◽  
Variable Degree ◽  
Circular Trajectory ◽  
Spatial Mechanism ◽  
Spatial Mechanisms ◽  
Motion Modes ◽  
Multi Mode ◽  
Motion Mode

Abstract This paper deals with the construction and reconfiguration analysis of a spatial mechanism composed of four circular translation (G) joints. Two links connected by a G joint, which can be in different forms such as a planar parallelogram, translate along a circular trajectory with respect to each other. A spatial 4G mechanism, which is composed of four G joints, usually has 1-DOF (degree-of-freedom). Firstly, a 2-DOF 4G mechanism is constructed. Then a novel variable-DOF spatial 4G mechanism is constructed starting from the 2-DOF 4G mechanism using the approach based on screw theory. Finally, the reconfiguration analysis is carried out in the configuration space using dual quaternions. The analysis shows that the variable-DOF spatial 4G mechanism has one 2-DOF motion mode and one to two 1-DOF motion modes and reveals how the 4G mechanism can switch among these motion modes. By removing one link from two adjacent G joints each and two links from each of the remaining two G joints, we can obtain a queer-rectangle and a queer-parallelogram, which are the generalization of the queer-square or derivative queer-square in the literature. The approach in this paper can be extended to the analysis of other types of coupled mechanisms using cables and gears and multi-mode spatial mechanisms involving G joints.

Variable degree-of-freedom spatial mechanisms composed of four circular translation joints

2021 ◽  
pp. 1-16
Author(s):  
Xianwen Kong
Keyword(s):  
Algebraic Geometry ◽  
Screw Theory ◽  
Degree Of Freedom ◽  
Variable Degree ◽  
Circular Trajectory ◽  
Spatial Mechanism ◽  
Spatial Mechanisms ◽  
Motion Modes ◽  
Multi Mode ◽  
Motion Mode

Abstract This paper deals with the construction and reconfiguration analysis of a spatial mechanism composed of four circular translation (G) joints. Two links connected by a G joint, which can be in different forms such as a planar parallelogram, translate along a circular trajectory with respect to each other. A spatial 4G mechanism, which is composed of four G joints, usually has 1-DOF (degree-of-freedom). Firstly, a 2-DOF spatial 4G mechanism is constructed. Then a novel variable-DOF spatial 4G mechanism is constructed starting from the 2-DOF 4G mechanism using the approach based on screw theory. Finally, the reconfiguration analysis is carried out in the configuration space using dual quaternions and tools from algebraic geometry. The analysis shows that the variable-DOF spatial 4G mechanism has one 2-DOF motion mode and one to two 1-DOF motion modes and reveals how the 4G mechanism can switch among these motion modes. By removing one link from two adjacent G joints each and two links from each of the remaining two G joints, we can obtain a queer-rectangle and a queer-parallelogram, which are the generalization of the queer-square or derivative queer-square in the literature. The approach in this paper can be extended to the analysis of other types of coupled mechanisms using cables and gears and multi-mode spatial mechanisms involving G joints.

scholarly journals Reconfiguration Analysis of an RRRRS Single-Loop Mechanism

Robotics ◽  
2018 ◽  
Vol 7 (3) ◽  
pp. 51
Author(s):  
Maurizio Ruggiu ◽  
Xianwen Kong
Keyword(s):  
Numerical Solutions ◽  
Motion Equation ◽  
Degree Of Freedom ◽  
Solid Model ◽  
Variable Degree ◽  
Single Loop ◽  
Motion Modes ◽  
The One ◽  
Classical Vector ◽  
First Time

The paper deals with the reconfiguration analysis of the single-loop variable degree-of-freedom (DOF) RRRRS mechanism composed of five links connected by four revolute (R) joints and one spherical (S) joint. The mechanism may show two modes of motion: one-DOF and two-DOF motion. In the paper, a classical vector procedure is used to obtain the quartic motion equation (QME) that allows one to inspect the nature of the motion. In general, the solutions of the QME provide the one-DOF motion of the mechanism except when all the coefficients of the equation vanish. In this case, the mechanism undergoes the two-DOF motion. The motion of the mechanism built according to two specific architectures was analyzed by the numerical solutions of the QME and with the help of the solid model of the mechanism. It is revealed for the first time that the perpendicular architecture has one 2-DOF motion and two 1-DOF motion modes.

Research on a Variable Degree of Freedom Luffing Mechanism, Part I

2013 ◽  
Vol 842 ◽  
pp. 433-438
Author(s):  
Xiao Guang Yao ◽  
Yong Bao Feng ◽  
Xiao Song Guo ◽  
Chang Lin Ma
Keyword(s):  
Degrees Of Freedom ◽  
Work Conditions ◽  
Degree Of Freedom ◽  
Dynamic Equations ◽  
Variable Degree ◽  
Analytic Model ◽  
Body System ◽  
Electric Control ◽  
Engineering Requirement ◽  
Relationship Of

According to the special engineering requirement, a novel luffing mechanism with variable degree of freedom is presented in this study. The mechanism is assumed to be an ideal rigid body system and the degrees of freedom in different work conditions are calculated. Then the kinematic equations of mechanism are obtained by the geometrical and motional relationship of the components; meanwhile, the dynamic equations of mechanism are deduced by the Newton's mechanical law. The analytic model can be employed for the calculation and analysis of the mechanism features; furthermore, it can be used for the design of hydraulic and electric control system.

scholarly journals Spatial Mechanism Design in Virtual Reality With Networking

2001 ◽  
Author(s):  
John N. Kihonge ◽  
Judy M. Vance ◽  
Pierre M. Larochelle
Keyword(s):  
Virtual Reality ◽  
Finite Sequence ◽  
Degree Of Freedom ◽  
Three Dimensions ◽  
Synthesis Process ◽  
Spatial Mechanisms ◽  
Cylindrical Joint ◽  
In Series ◽  
Simply Connected ◽  
Two Degree Of Freedom

Abstract Mechanisms are used in many devices to move a rigid body through a finite sequence of prescribed locations in space. The most commonly used mechanisms are four-bar planar mechanisms that move an object in one plane in space. Spatial mechanisms allow motion in three-dimensions (3D). Spatial 4C mechanisms are two degree of freedom kinematic closed-chains consisting of four rigid links simply connected in series by cylindrical (C) joints. A cylindrical joint is a two degree of freedom joint which allows translation along and rotation about a line in space. This paper describes a synthesis process for the design of 4C spatial mechanisms in a virtual environment. Virtual reality allows the user to view and interact with digital models in a more intuitive way than using the traditional human-computer interface (HCI). The software developed as part of this research also allows multiple users to network and share the designed mechanism. Networking tools have the potential to greatly enhance communication between members of the design team at different industrial sites and therefore reduce design costs.

Solution of Topology Embryonic Graph and Topology Graph for Unified Planar-Spatial Mechanisms

2003 ◽  
Author(s):  
Lu Yi ◽  
Tatu Leinonen
Keyword(s):  
Degrees Of Freedom ◽  
Degree Of Freedom ◽  
Matrix Approach ◽  
Group Approach ◽  
Spatial Mechanism ◽  
Spatial Mechanisms ◽  
And Topology ◽  
Topology Graph ◽  
Relative Theory

An analysis matrix approach for solving an isomeric topology embryonic graph and a digital group approach for solving an isomeric topology graph of a unified planar-spatial mechanism are presented and the relative theory is discussed. Firstly, all binary links are removed from each acceptable linkage system with different degrees of freedom, many analysis matrixes are constructed, and many topology embryonic graphs of the mechanism are derived. Secondly, from an acceptable multi-element link combination of planar or spatial mechanisms, a rule for determining the isomeric topology embryonic graphs and an unreasonable topology embryonic graph is obtained. Thirdly, by considering the degree of freedom of the mechanism and the configuration of a planar or spatial mechanism, the number of binary links is determined. Finally, all removed binary links are rearranged systematically back into an isomeric topology embryonic graph, and the acceptable topology graphs of the mechanism are derived by using a digital group approach. Some illustrations show that the two approaches are simple and effective tools and can be employed to synthesize both planar and spatial mechanisms.

Interruption performance design of variable freedom mechanism triggered by electro-mechanical-magnetic coupling

2016 ◽  
Vol 231 (18) ◽  
pp. 3330-3341 ◽  
Author(s):  
Jinghua Xu ◽  
Shuyou Zhang ◽  
Jianrong Tan ◽  
Sheng Hongsheng
Keyword(s):  
Degrees Of Freedom ◽  
Magnetic Coupling ◽  
Radiation Energy ◽  
Degree Of Freedom ◽  
Design Parameters ◽  
Coupling Mechanism ◽  
Variable Degree ◽  
Algebraic Equations ◽  
Tightening Force ◽  
Linear Algebraic Equations

Coupling mechanism plays an important role in transmitting, motivating and actuating mechanical functions. However, it is difficult to obtain the transient dynamics performance of mechanism with variable degree of freedom precisely. Therefore, an interruption performance design method of variable freedom mechanism triggered by electro-magneto-thermo coupling is put forward. The Euler-Lagrange partial differential equations of variable freedom mechanism are built using generalized coordinates. Degree of freedom reduction rules are proposed to merge transformation or rotation constraints and obtain the total degrees of freedom of variable freedom mechanism at each transient status. Bivariate interpolating is employed to determine the electro-mechanical-magnetic coupled Lorentz force. Dynamics performance is simulated by iteration of linear algebraic equations using implicit predictor-corrector integration method. The design parameters such as stiffness and pre-tightening force of trigger spring, permissible dimension deviations and hole-shaft fit tolerance are determined and improved using the sensitivity analysis of simulation results. The pneumatic mechanical endurance and thermal infrared temperature rise experiments are accomplished to determine the infrared radiation energy distribution and transient working status of components. It gives an auxiliary thermo-visual approach for transient performance design of coupling mechanism.

Design of One Degree of Freedom Closed Loop Spatial Chains Using Non-Circular Gears

2009 ◽  
Author(s):  
Mandar Harshe ◽  
Carl Crane ◽  
David B. Dooner
Keyword(s):  
Joint Space ◽  
Optimization Techniques ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
End Effector ◽  
Starting Position ◽  
Position Errors ◽  
Spatial Mechanisms ◽  
Error Functional ◽  
Systems Of Polynomial Equations

This paper presents the design of one degree-of-freedom spatial mechanisms that use non-circular gears to constrain the motion. In a spatial body-guidance problem, representing the motion by systems of polynomial equations restricts the number of end-effector positions and orientations (end-effector poses) that can be used as inputs for mechanism design. An approach has been developed that takes any number of desired poses as guide points and develops a mechanism that approximately attains the desired poses over the course of its motion. A problem with implementing this design strategy is the inherent difficulty in accounting for orientation and position errors. The approach described here addresses this problem by defining a new error functional, calculated in the joint space domain. As the mechanisms being dealt with are single degree-of-freedom closed chains, the starting position is a crucial decision in the design process. The method outlines the choice of the starting position and details how this error term can be used along with optimization techniques on either the mechanism parameters or the non-circular gears. A numerical example is presented.

Four-Position Synthesis for Spatial Mechanisms With Two Independent Loops

1992 ◽  
Author(s):  
Chien H. Chiang ◽  
Wei Hua Chieng ◽  
David A. Hoeltzel
Keyword(s):  
Rigid Body ◽  
Mathematical Models ◽  
Analytical Methods ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Practical Applications ◽  
Single Degree ◽  
Spatial Mechanisms ◽  
Position Synthesis ◽  
Independent Loops

Abstract Mathematical models that have been employed to synthesize spatial mechanisms for rigid body guidance have been found to be too complicated to implement in practical applications, especially for four-position guidance synthesis. This paper describes simple analytical methods for synthesizing single degree-of-freedom spatial mechanisms having two independent loops for four precision positions. In addition, prescribed timing has been simultaneously considered for several spatial mechanisms.

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