Virtual Chain Approach for Mobility Analysis of Multiloop Deployable Mechanisms

2013 ◽  
Vol 135 (11) ◽  
Author(s):  
Hailin Huang ◽  
Zongquan Deng ◽  
Xiaozhi Qi ◽  
Bing Li
Keyword(s):  
Relative Motion ◽  
Twist Angle ◽  
Open Loop ◽  
Mobility Analysis ◽  
Link Length ◽  
Flexible Links ◽  
Single Loop ◽  
Kinematic Chains ◽  
In Series ◽  
Insight Into

In this paper, we present a virtual chain approach for the mobility analysis of multiloop deployable mechanisms. First, the relative motion of the links of single-loop units in multiloop mechanisms are analyzed using the equivalent motion of certain types of open-loop virtual kinematic chains; these kinematic chains comprise some types of joints connected in series by flexible links. This reveals that the links in these virtual chains are not rigid when the mechanism is moving. The parameters of these virtual kinematic chains (such as the link length, the twist angle of two adjacent revolute joint axes, and so on) are variable. By using this approach that involves equivalent kinematic chains, the multiloop mechanisms can be considered equivalent to single-loop mechanisms with flexible links; the closure equations of such multiloop mechanisms can also be derived. The analytical procedures are explained using examples of multiloop mechanisms in which Myard mechanisms as used as the basic single-loop units. A prototype is also fabricated to demonstrate the feasibility of the proposed multiloop mechanism. The proposed method yields a more intuitive and straightforward insight into the mobility of complicated multiloop mechanisms.

Mobility of Single Loop Linkages: A Final Word?

2007 ◽  
Author(s):  
Jose´ Mari´a Rico ◽  
J. Jesu´s Cervantes ◽  
Juan Rocha ◽  
Jaime Gallardo ◽  
Luis Daniel Aguilera ◽  
...  
Keyword(s):  
Mobility Analysis ◽  
Additional Insight ◽  
Final Word ◽  
Single Loop ◽  
Kinematic Chains ◽  
Recent Developments ◽  
The Subject ◽  
Insight Into

Setting aside paradoxical linkages such as Bennett’s, Bricard’s or Goldberg’s, the mobility of single loop linkages seemed, with the developments on mobility analysis carried out in the last five years, a closed chapter in kinematic research. However, recent developments on the mobility of parallel platforms have shed additional insight into the problem. This contribution attempts to unify the results obtained in the last five years in the area of mobility of single-loop kinematic chains to state what appears to be a final word on the subject.

Topological Synthesis of Geared Robotic Mechanism

1996 ◽  
Author(s):  
Dar-Zen Chen ◽  
Shuen-Chen Shieu
Keyword(s):  
Transmission Lines ◽  
Open Loop ◽  
Mechanical Transmission ◽  
Kinematic Structure ◽  
Input Unit ◽  
Kinematic Chains ◽  
Systematic Methodology ◽  
In Series ◽  
Novel Structures ◽  
Topological Synthesis

Abstract An efficient and systematic methodology for the topological synthesis of geared robotic mechanisms is developed. The approach is based on the idea that the kinematic structure of a geared robotic mechanism can be described by an equivalent open-loop chain (EOLC) and mechanical transmission lines (MTLs) which drive the joints of the EOLC. It is shown that an MTL can be decomposed as an input unit and several transmission units connected in series. The characteristics of the input and transmission units are laid out and a systematic methodology is developed to enumerate all admissible input and transmission units from the existing atlas of non-fractionated geared kinematic chains. The atlas of admissible MTLs are then generated accordingly. Thus, all admissible geared robotic mechanisms can be enumerated efficiently with the atlas of admissible MTLs and a preferred form of the EOLC. With this new methodology, some novel structures of geared robotic mechanisms are obtained and it is believed that new areas of application can be further explored.

A Systematic Formulation of Overconstraint Conditions in Kinematic Chains by Displacement Groups

2005 ◽  
Author(s):  
Carlo Galletti ◽  
Pietro Fanghella ◽  
Elena Giannotti
Keyword(s):  
Dynamic Analysis ◽  
Systematic Approach ◽  
Computer Code ◽  
Computer Implementation ◽  
Mobility Analysis ◽  
Kinematic Synthesis ◽  
Single Loop ◽  
Kinematic Chains ◽  
Geometric Data ◽  
Systematic Formulation

The paper describes a systematic approach to define geometrical and dimensional overconstraint conditions for single-loop kinematic chains of both “banal” and “exceptional” types. The approach is an application of the theory of displacement groups. It presents several interesting features: it can be easily integrated with mobility analysis; it makes use of geometric data local to links and does not require a preliminary mechanism assembly nor a given initial congruent position; it is systematic and can be suitably implemented in a computer code; it suggests where geometrical and dimensional tolerances have to be located; it can be embedded in other group-based approaches, like kinematic synthesis or dynamic analysis. After a brief summary of the properties of displacement groups and their operations, the paper shows how they can be used to formulate systematically the overconstraint conditions in kinematic chains. A computer implementation of the approach is also outlined, and several examples with different complexities are given.

Mobility Analysis of Symmetric Deployable Mechanisms Involved in a Coplanar 2-Twist Screw System

2015 ◽  
Vol 8 (1) ◽  
Author(s):  
Bing Li ◽  
Hailin Huang ◽  
Zongquan Deng
Keyword(s):  
Traditional Approach ◽  
Mobility Analysis ◽  
Kinematic Chains ◽  
Insight Into

In this paper, an intuitive approach for the mobility analysis of deployable mechanisms involved in a special screw system with two coplanar twist vectors is proposed. First, the coplanar screw system with a pair of parallel/concurrent zero pitch screws is analyzed, and the intuitive allowable mobility set for the screw system is described. Next, kinematic chains containing the coplanar screw system are enumerated. The proposed approach is used to explain the mobility of the deployable Bennett mechanism, Myard mechanism, and Bricard mechanism; some novel deployable mechanisms could be found based on the analysis. Furthermore, it is shown that the proposed approach can be applied to the mobility analysis of multiloop deployable mechanisms and is found to be more intuitive than the traditional approach, which provides a straightforward insight into the mobility of complicated mechanisms.

Mobility Analysis of Parallel Mechanisms Based on Screw Theory and the Concept of Equivalent Serial Kinematic Chain

2005 ◽  
Author(s):  
Xianwen Kong ◽  
Cle´ment M. Gosselin
Keyword(s):  
Systematic Approach ◽  
Screw Theory ◽  
Kinematic Chain ◽  
Second Step ◽  
Parallel Mechanisms ◽  
Mobility Analysis ◽  
Single Loop ◽  
Kinematic Chains ◽  
Serial Chain ◽  
Parallel Kinematic

This paper presents a systematic approach for the mobility analysis of parallel mechanisms. The method is based on screw theory and the concept of equivalent serial chain. An equivalent serial kinematic chain of a k-legged PKC (parallel kinematic chain) is defined as a serial kinematic chain which has the same twist system and the wrench system as the k-legged PKC. Using the proposed approach, the mobility analysis of a PKC is performed in two steps. The first step is the instantaneous mobility analysis, and the second step is the full-cycle mobility inspection. The first step is dealt with based on screw theory. The second step is performed with the aid of the concept of equivalent serial chain and the types of multi-DOF overconstrained single-loop kinematic chains. The proposed approach is illustrated with several examples.

Kinematic Modeling and Inverse Kinematics of Serial 6R Fragment of Molecule

2021 ◽  
Author(s):  
Keisuke Arikawa
Keyword(s):  
Inverse Kinematics ◽  
Twist Angle ◽  
Structural Data ◽  
Data Bank ◽  
Kinematic Modeling ◽  
Link Length ◽  
Dna And Rna ◽  
Revolute Joints ◽  
In Series ◽  
Multiple Conformations

Abstract Depending on their mobilities around bond axes, molecules (e.g., proteins, DNA, and RNA) can be modeled as robotic manipulators. We focus on the serial 6R fragments, or the fragments containing six revolute joints connected in series, extracted from these molecules. We solved the inverse kinematics problems of the fragments. We obtained multiple conformations that maintained the relative position and orientation between both ends. Raghavan and Roth’s solution effectively conveys all real solutions. However, the solution is not directly applicable when some link lengths are zeros. To cope with the problem, in addition to the known method based on the modified elimination, we introduced the small-length link strategy. Here, by setting sufficiently small values for the zero-length links, we solved the inverse kinematics problems based on Raghavan and Roth’s solution combined with the symbolic formulation. Moreover, we formulated a method to systematically build manipulator models from structural data of molecules. We systematically identified the Danavit-Hartenberg parameters (link length, offset, and twist angle) and joint angles at the conformation in the structural data from the seven pairs of positions of atoms. Finally, using the structural data of a protein stored in the protein data bank, we demonstrated an application example of kinematic modeling and inverse kinematics calculation.

Synthesis of Deployable/Foldable Single Loop Mechanisms With Revolute Joints

2011 ◽  
Vol 3 (3) ◽  
Author(s):  
Zongquan Deng ◽  
Hailin Huang ◽  
Bing Li ◽  
Rongqiang Liu
Keyword(s):  
Computer Aided Design ◽  
Geometric Approach ◽  
Mobility Analysis ◽  
Design Models ◽  
Single Loop ◽  
Kinematic Chains ◽  
Design And Synthesis ◽  
Revolute Joints ◽  
Computer Aided ◽  
Aided Design

This paper presents a geometric approach for design and synthesis of deployable/foldable single loop mechanisms with pure revolute joints. The basic kinematic chains with symmetric mobility are first synthesized, and an intuitive geometric method is proposed for the mobility analysis of these kinematic chains. The deployable/foldable single loop mechanisms can be regarded as a combination of the basic kinematic chains with nontrivial mobility intersection, under this approach, the 5R to 8R single loop mechanisms with symmetric mobility are synthesized systematically. The method for determining the positions of the joint axes on polyhedral links is also proposed, so that the mechanism can be fully deployed or fully folded without suffering from physical interference. Under this framework, a class of novel deployable/foldable single loop mechanisms is developed. The computer-aided design models for typical examples are built to illustrate their feasibility.

Topological Synthesis of Geared Robotic Mechanisms

1998 ◽  
Vol 120 (2) ◽  
pp. 230-239 ◽  
Author(s):  
Dar-Zen Chen ◽  
Shuen-Chen Shiue
Keyword(s):  
Transmission Lines ◽  
Open Loop ◽  
Mechanical Transmission ◽  
Kinematic Structure ◽  
Input Unit ◽  
Kinematic Chains ◽  
Systematic Methodology ◽  
In Series ◽  
Novel Structures ◽  
Topological Synthesis

An efficient and systematic methodology for the topological synthesis of geared robotic mechanisms is developed. The approach is based on the idea that the kinematic structure of a geared robotic mechanism can be described by an equivalent open-loop chain (EOLC) and mechanical transmission lines (MTLs) which drive the joints of the EOLC. It is shown that an MTL can be decomposed as an input unit and several transmission units connected in series. The characteristics of the input and transmission units are laid out and a systematic methodology is developed to enumerate all admissible input and transmission units from the existing atlas of nonfractionated geared kinematic chains. The atlas of admissible MTLs are then generated accordingly. Thus, all admissible geared robotic mechanisms can be enumerated efficiently with the atlas of admissible MTLs and a preferred form of the EOLC. With this new methodology, some novel structures of geared robotic mechanisms are obtained and it is believed that new areas of application can be further explored.

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.

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