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.

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.

A Novel Method for Constructing Multi-Mode Deployable Polyhedron Mechanisms Using Symmetric Spatial RRR Compositional Units

2018 ◽  
Author(s):  
Jieyu Wang ◽  
Xianwen Kong
Keyword(s):  
Kinematic Chain ◽  
Degree Of Freedom ◽  
Single Loop ◽  
Kinematic Chains ◽  
The Third ◽  
Motion Modes ◽  
3D Printed ◽  
Novel Method ◽  
Multi Mode ◽  
Motion Mode

A novel construction method is proposed to construct multimode deployable polyhedron mechanisms (DPMs) using symmetric spatial RRR compositional units, a serial kinematic chain in which the axes of the first and the third revolute (R) joints are perpendicular to the axis of the second R joint. Single-loop deployable linkages are first constructed using RRR units and are further assembled into polyhedron mechanisms by connecting single-loop kinematic chains using RRR units. The proposed mechanisms are over-constrained and can be deployed through two approaches. The prism mechanism constructed using two Bricard linkages and six RRR limbs has one degree-of-freedom (DOF). When removing three of the RRR limbs, the mechanism obtains one additional 1-DOF motion mode. The DPMs based on 8R and 10R linkages also have multiple modes, and several mechanisms are variable-DOF mechanisms. The DPMs can switch among different motion modes through transition positions. Prototypes are 3D-printed to verify the feasibility of the mechanisms.

A Single-Loop 7R Spatial Mechanism That Has Three Motion Modes With the Same Instantaneous DOF but Different Finite DOF

2018 ◽  
Author(s):  
Xianwen Kong ◽  
Andreas Müller
Keyword(s):  
Higher Order ◽  
Mobility Analysis ◽  
Single Loop ◽  
Plane Symmetric ◽  
Spatial Mechanism ◽  
Motion Modes ◽  
Regular Configuration ◽  
Kinematic Loop ◽  
Multi Mode ◽  
Motion Mode

Multi-mode mechanisms, including kinematotropic mechanisms, are a class of reconfigurable mechanisms that can switch motion modes with the same or different DOF (degree-of-freedom). For most of the multi-mode mechanisms reported in the literature, the instantaneous (or differential) DOF and finite DOF in a motion mode are equal. In this paper, we will discuss the construction, reconfiguration analysis, and higher-order mobility analysis of a multi-mode single-loop 7R mechanism that has three motion modes with the same instantaneous DOF but different finite DOF. Firstly, the novel multi-mode single-loop 7R spatial mechanism is constructed by inserting one revolute (R) joint into a plane symmetric Bennett joint-based 6R mechanism for circular translation. The reconfiguration analysis is then carried out in the configuration space by solving a set of kinematic loop equations based on dual quaternions and the natural exponential function substitution using tools from algebraic geometry. The analysis shows that the multi-mode single-loop 7R spatial mechanism has three motion modes, including a 2-DOF planar 5R mode and two 1-DOF spatial 6R modes and can transit between each pair of motion modes through two transition configurations. The higher-order mobility analysis shows that the 7R mechanism has two-instantaneous DOF at a regular configuration of any motion mode and three instantaneous DOF in a transition configuration. The infinitesimal motions that are not tangential to finite motions are of second-order in transition configurations between 2-DOF motion mode 1 and 1-DOF motion modes 2 or 3 or first-order in transition configurations between 1-DOF motion modes 2 and 3.

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.

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.

A reconfigurable tri-prism mobile robot with eight modes

Robotica ◽  
2018 ◽  
Vol 36 (10) ◽  
pp. 1454-1476 ◽  
Author(s):  
Jieyu Wang ◽  
Yan'an Yao ◽  
Xianwen Kong
Keyword(s):  
Mobile Robot ◽  
3D Model ◽  
Screw Theory ◽  
Degree Of Freedom ◽  
Biped Robots ◽  
Wheeled Robots ◽  
Motion Mode ◽  
Kinematic Properties

SUMMARYA novel reconfigurable tri-prism mobile robot with eight modes is proposed. The robot is composed of two feet connected by three U-R-U (universal-revolute-universal) limbs. The robot incorporates the kinematic properties of sphere robots, squirming robots, tracked robots, wheeled robots and biped robots. In addition, the somersaulting and turning modes are also explored. After the description of the robot, the DOF (degree-of-freedom) is calculated based on screw theory. The 3D model and simulations indicate that the robot can cross several typical obstacles and can also be folded via two approaches. Finally, the prototype experiments are presented to verify the feasibility of the proposed mobile robot in different motion mode.

scholarly journals Random Forest Algorithm with a Half-Voting and Weighted Decision Trees for Interior Pedestrian Tracking

2019 ◽  
Vol 8 (3) ◽  
pp. 6971-6976
Keyword(s):  
Random Forest ◽  
Decision Trees ◽  
Field Experiments ◽  
Threshold Value ◽  
Pedestrian Tracking ◽  
Zero Velocity ◽  
Motion Modes ◽  
Multi Mode ◽  
Motion Mode ◽  
Selection Of

The traditional Zero Velocity Updating Algorithm is being used to correct the accumulated errors of the device effectively. However, as the threshold value of the traditional Zero Velocity Updating algorithm is fixed, it is only suitable for a single motion mode. When indoor pedestrian motion includes multiple motion modes, the positioning accuracy will be greatly reduced. In this paper, we propose an adaptive Zero Velocity Updating method for multi-motion mode using half- voting Random Forest. We analysed the selection of Zero Velocity Updating threshold value for stilling, walking, running, going upstairs and downstairs for the interior pedestrian. Then we recognize pedestrian motion by Random Forest with a Half-Voting and Weighted Decision Trees. Finally according to the result of recognition adjust the threshold adaptively to determine the zero velocity intervals accurately. In order to verify the feasibility and effectiveness of the method proposed in this paper, field experiments were carried out with the inertial navigation module developed by our laboratory. The experimental results show that when indoor pedestrians perform multi-mode motion, the positioning error is 0.5m.

Kinematic Analysis of Conventional and Multi-Mode Spatial Mechanisms Using Dual Quaternions

2016 ◽  
Author(s):  
Xianwen Kong
Keyword(s):  
Algebraic Geometry ◽  
Kinematic Analysis ◽  
Fundamental Issue ◽  
Input Output ◽  
Plane Symmetric ◽  
Spatial Mechanism ◽  
Dual Quaternions ◽  
Reconfigurable Mechanisms ◽  
Kinematic Loop ◽  
Multi Mode

Although kinematic analysis of conventional mechanisms is a well-documented fundamental issue in mechanisms and robotics, the emerging reconfigurable mechanisms and robots (or mechanisms and robots with multiple operation modes) require re-examining this fundamental issue. Recent advances in mathematics, especially algebraic geometry and numerical algebraic geometry, make it possible to develop an efficient method for the kinematic analysis of not only conventional mechanisms and robots but also reconfigurable mechanisms and robots. This paper first presents a method for setting up a set of kinematic loop equations for mechanisms using dual quaternions. Using this approach, a set of kinematic loop equations of a spatial mechanism is composed of six equations. The effectiveness of the proposed kinematic loop equations is then demonstrated by deriving the explicit input-output equations of a line symmetric 1-DOF (degree-of-freedom) 7R single-loop spatial mechanism, the re-configuration analysis of a novel multi-mode 1-DOF 7R spatial mechanism. In the former case, an explicit input-output equation of degree 8 is derived. In the latter case, it is found that the 7R multi-mode mechanism has three motion modes, including a planar 4R mode, an orthogonal Bricard 6R mode, and a plane symmetric 6R mode. Unlike the 7R multi-mode mechanisms in the literature, the 7R multi-mode mechanism presented in this paper does not have a 7R mode in which all the seven R joints can move simultaneously.

Reconfiguration Analysis of Multimode Single-Loop Spatial Mechanisms Using Dual Quaternions

2017 ◽  
Vol 9 (5) ◽  
Author(s):  
Xianwen Kong
Keyword(s):  
Algebraic Geometry ◽  
Single Degree Of Freedom ◽  
Plane Symmetric ◽  
Dual Quaternions ◽  
Revolute Joints ◽  
Spatial Mechanisms ◽  
Reconfigurable Mechanisms ◽  
Motion Modes ◽  
Kinematic Loop ◽  
And Robotics

Although kinematic analysis of conventional mechanisms is a well-documented fundamental issue in mechanisms and robotics, the emerging reconfigurable mechanisms and robots pose new challenges in kinematics. One of the challenges is the reconfiguration analysis of multimode mechanisms, which refers to finding all the motion modes and the transition configurations of the multimode mechanisms. Recent advances in mathematics, especially algebraic geometry and numerical algebraic geometry, make it possible to develop an efficient method for the reconfiguration analysis of reconfigurable mechanisms and robots. This paper first presents a method for formulating a set of kinematic loop equations for mechanisms using dual quaternions. Using this approach, a set of kinematic loop equations of spatial mechanisms is composed of six polynomial equations. Then the reconfiguration analysis of a novel multimode single-degree-of-freedom (1DOF) 7R spatial mechanism is dealt with by solving the set of loop equations using tools from algebraic geometry. It is found that the 7R multimode mechanism has three motion modes, including a planar 4R mode, an orthogonal Bricard 6R mode, and a plane symmetric 6R mode. Three (or one) R (revolute) joints of the 7R multimode mechanism lose their DOF in its 4R (or 6R) motion modes. Unlike the 7R multimode mechanisms in the literature, the 7R multimode mechanism presented in this paper does not have a 7R mode in which all the seven R joints can move simultaneously.

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