Structure Synthesis and Reconfiguration Analysis of Variable-DOF Single-Loop Mechanisms With Prismatic Joints Using Dual Quaternions

2021 ◽  
pp. 1-26
Author(s):  
Kai Liu ◽  
Jingjun Yu ◽  
Xianwen Kong
Keyword(s):  
Algebraic Method ◽  
Variable Degree ◽  
Prime Decomposition ◽  
Single Loop ◽  
Dual Quaternions ◽  
Motion Modes ◽  
Structure Synthesis ◽  
Prismatic Joints ◽  
Kinematic Mapping ◽  
Motion Mode

Abstract This paper deals with the structure synthesis and reconfiguration analysis of variable-DOF (variable degree-of-freedom) single-loop mechanisms with prismatic joints based on a unified tool - the dual quaternion. According to motion polynomials over dual quaternions, an algebraic method is presented to synthesize variable-DOF single-loop 5R2P mechanisms (R and P denote revolute and prismatic joints respectively), which are composed of the Bennett and RPRP mechanisms. Using this approach, variable-DOF single-loop RRPRPRR and RRPRRPR mechanisms are constructed by joints obtained from the factorization of motion polynomials. Then reconfiguration analysis of these variable-DOF single-loop mechanisms is performed in light of the kinematic mapping and the prime decomposition. The results show that the variable-DOF 5R2P mechanisms have a 1-DOF spatial 5P2P motion mode and a 2-DOF Bennett-RPRP motion mode. Furthermore, the variable-DOF 5R2P mechanisms have two transition configurations, from which the mechanisms can switch among their two motion modes.

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.

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.

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 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.

A Novel Method for Constructing Multimode Deployable Polyhedron Mechanisms Using Symmetric Spatial Compositional Units

2019 ◽  
Vol 11 (2) ◽  
Author(s):  
Jieyu Wang ◽  
Xianwen Kong
Keyword(s):  
Kinematic Chain ◽  
Construction Method ◽  
Degree Of Freedom ◽  
Multiple Modes ◽  
Single Loop ◽  
The Third ◽  
Motion Modes ◽  
3D Printed ◽  
Novel Method ◽  
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 then assembled into polyhedron mechanisms by connecting the single-loop linkages using RRR units. The proposed mechanisms are over-constrained and can be deployed. The prism mechanism constructed using two Bricard linkages and six RRR chains has one degree-of-freedom (DOF). When removing three of the RRR chains, the mechanism will have one additional 1-DOF motion mode. The DPMs based on 8R and 10R linkages also have multiple modes, and several mechanisms have variable-DOF. The DPMs can switch among different motion modes through transition positions. Prototypes are 3D-printed to verify the feasibility of the mechanisms.

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.

Mobility of Single-Loop N-Bar Linkage With Active/Passive Prismatic Joints

2005 ◽  
Vol 128 (6) ◽  
pp. 1261-1271 ◽  
Author(s):  
W. Z. Guo ◽  
R. Du
Keyword(s):  
Open Loop ◽  
Class Iii ◽  
Active Joint ◽  
Revolute Joint ◽  
Single Loop ◽  
Prismatic Joint ◽  
Passive Joint ◽  
Offset Distance ◽  
Prismatic Joints ◽  
Planar Linkages

Single-loop N-bar linkages that contain one prismatic joint are common in engineering. This type of mechanism often requires complicated control and, hence, understanding its mobility is very important. This paper presents a systematic study on the mobility of this type of mechanism by introducing the concept of virtual link. It is found that this type of mechanism can be divided into three categories: Class I, Class II, and Class III. For each category, the slide reachable range is cut into different regions: Grashof region, non-Grashof region, and change-point region. In each region, the rotation range of the revolute joint or rotatability of the linkage can be determined based on Ting’s criteria. The characteristics charts are given to describe the rotatability condition. Furthermore, if the prismatic joint is an active joint, the revolvability of the input revolute joint is dependent in non-Grashof region but independent in other regions. If the prismatic joint is a passive joint, the revolvability of the input revolute joint is dependent on the offset distance of the prismatic joint. Two examples are given to demonstrate the presented method. The new method is able to cover all the cases of N-bar planar linkages with one or a set of adjoined prismatic joints. It can also be used to study N-bar open-loop planar robotic mechanisms.

scholarly journals Kinematic analysis of a single-loop reconfigurable 7R mechanism with multiple operation modes

Robotica ◽  
2014 ◽  
Vol 32 (7) ◽  
pp. 1171-1188 ◽  
Author(s):  
Xiuyun He ◽  
Xianwen Kong ◽  
Damien Chablat ◽  
Stéphane Caro ◽  
Guangbo Hao
Keyword(s):  
Kinematic Analysis ◽  
Computer Aided Design ◽  
Operation Mode ◽  
Algebraic Approach ◽  
Single Loop ◽  
Operation Modes ◽  
Translational Mode ◽  
Kinematic Mapping ◽  
Multiple Operation ◽  
Aided Design

SUMMARYThis paper presents a novel one-degree-of-freedom (1-DOF) single-loop reconfigurable 7R mechanism with multiple operation modes (SLR7RMMOM), composed of seven revolute (R) joints, via adding a revolute joint to the overconstrained Sarrus linkage. The SLR7RMMOM can switch from one operation mode to another without disconnection and reassembly, and is a non-overconstrained mechanism. The algorithm for the inverse kinematics of the serial 6R mechanism using kinematic mapping is adopted to deal with the kinematic analysis of the SLR7RMMOM. First, a numerical method is applied and an example is given to show that there are 13 sets of solutions for the SLR7RMMOM, corresponding to each input angle. Among these solutions, nine sets are real solutions, which are verified using both a computer-aided design (CAD) model and a prototype of the mechanism. Then an algebraic approach is also used to analyse the mechanism and same results are obtained as the numerical one. It is shown from both numerical and algebraic approaches that the SLR7RMMOM has three operation modes: a translational mode and two 1-DOF planar modes. The transitional configurations among the three modes are also identified.

Velocity, Acceleration, and Static-Force Analyses of Spatial Linkages

1965 ◽  
Vol 32 (4) ◽  
pp. 903-910 ◽  
Author(s):  
J. Denavit ◽  
R. S. Hartenberg ◽  
R. Razi ◽  
J. J. Uicker
Keyword(s):  
Virtual Work ◽  
Algebraic Method ◽  
Degree Of Freedom ◽  
Static Force ◽  
Virtual Displacement ◽  
Single Loop ◽  
Loop Equation ◽  
The Matrix ◽  
Spatial Linkages

The algebraic method using 4 × 4 matrices is extended to the analysis of velocities, accelerations, and static forces in one-degree-of-freedom, single-loop, spatial linkages consisting of revolute and prismatic pairs, either singly or in combination. The methods are well suited for machine calculations and have been tested on a number of examples, one of which is presented. Velocities and accelerations are obtained by differentiation of the matrix-loop or position equation. Static forces are found by combining the method of virtual work with the matrix-loop equation to relate the virtual displacement of the load to given virtual deformations of the links.

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