Solving the Input/Output Problem for Planar Mechanisms

1998 ◽  
Author(s):  
James Nielsen ◽  
Bernard Roth
Keyword(s):  
Solution Procedure ◽  
Polynomial Equations ◽  
Input Output ◽  
Planar Mechanisms ◽  
Revolute Joints

Abstract This paper presents a method for solving the input/output problem for all planar mechanisms composed of revolute joints. The solution procedure is a modification of the Dixon resultant method, which was developed to solve sets of polynomial equations; in this paper the method is applied to sets of equations which are linear in the sines and cosines of unknown angles. A particular planar multi-circuit mechanism is analyzed to illustrate the solution procedure, and implementation details are discussed.

Solving the Input/Output Problem for Planar Mechanisms

1999 ◽  
Vol 121 (2) ◽  
pp. 206-211 ◽  
Author(s):  
J. Nielsen ◽  
B. Roth
Keyword(s):  
Solution Procedure ◽  
Polynomial Equations ◽  
Input Output ◽  
Planar Mechanisms

This paper presents a method for solving the input/output problem for all planar mechanisms composed of revolute and slider joints. The solution procedure is a modification of the Dixon resultant method, which was developed to solve sets of polynomial equations; in this paper the method is applied to sets of equations which are linear in the sines and cosines of unknown angles. A particular planar multicircuit mechanism is analyzed to illustrate the solution procedure, and implementation details are discussed.

Solving the Kinematics of Planar Mechanisms

1998 ◽  
Author(s):  
Charles W. Wampler
Keyword(s):  
Eigenvalue Problem ◽  
Complex Plane ◽  
System Of Equations ◽  
Polynomial Equations ◽  
Input Output ◽  
Planar Mechanisms ◽  
General Method

Abstract This paper presents a general method for the analysis of planar mechanisms consisting of rigid links connected by rotational and/or translational joints. After describing the links as vectors in the complex plane, a simple recipe is outlined for formulating a set of polynomial equations which determine the locations of the links when the mechanism is assembled. It is then shown how to reduce this system of equations to a standard eigenvalue problem, or if preferred, a single resultant polynomial. Both input/output problems and tracing-curve equations are treated.

scholarly journals Solving the Kinematics of Planar Mechanisms by Dixon Determinant and a Complex-Plane Formulation

2000 ◽  
Vol 123 (3) ◽  
pp. 382-387 ◽  
Author(s):  
Charles W. Wampler
Keyword(s):  
Eigenvalue Problem ◽  
Complex Plane ◽  
Numerical Solutions ◽  
Minimal Size ◽  
Input Output ◽  
Planar Mechanisms ◽  
Planar Mechanism ◽  
Revolute Joints ◽  
Generalized Eigenvalue ◽  
General Method

This paper presents a general method for the analysis of any planar mechanism consisting of rigid links connected by revolute joints. The method combines a complex plane formulation [1] with the Dixon determinant procedure of Nielsen and Roth [2]. The result is simple to derive and implement, so in addition to providing numerical solutions, the approach facilitates analytical explorations. The procedure leads to a generalized eigenvalue problem of minimal size. Both input/output problems and the derivation of tracing curve equations are addressed, as is the extension of the method to treat slider joints.

Solving the Kinematics of Planar Mechanisms

1999 ◽  
Vol 121 (3) ◽  
pp. 387-391 ◽  
Author(s):  
C. W. Wampler
Keyword(s):  
Eigenvalue Problem ◽  
Complex Plane ◽  
Generalized Eigenvalue Problem ◽  
System Of Equations ◽  
Polynomial Equations ◽  
Input Output ◽  
Planar Mechanisms ◽  
Generalized Eigenvalue ◽  
General Method

This paper presents a general method for the analysis of planar mechanisms consisting of rigid links connected by rotational and/or translational joints. After describing the links as vectors in the complex plane, a simple recipe is outlined for formulating a set of polynomial equations which determine the locations of the links when the mechanism is assembled. It is then shown how to reduce this system of equations to a generalized eigenvalue problem, or in some cases, a single resultant polynomial. Both input/output problems and tracing-curve equations are treated.

Kinematic Singularities of Free-Floating Open-Chain Planar Manipulators

1992 ◽  
Author(s):  
Sunil Kumar Agrawal ◽  
J. Rambhaskar
Keyword(s):  
Polynomial Equations ◽  
Joint Angles ◽  
Systematic Method ◽  
Open Chain ◽  
Singular Configurations ◽  
Revolute Joints ◽  
Planar Manipulators ◽  
Fixed Base ◽  
External Forces ◽  
Kinematic Singularities

Abstract This paper deals with Jacobian singularities of free-floating open-chain planar manipulators. The problem, in essence, is to find the joint angles where the Jacobian mapping between the end-effector rates and the joint rates is singular. In the absence of external forces and couples, for free-floating manipulators, the linear and angular momentum are conserved. This makes the singular configurations of free-floating manipulators different from structurally similar fixed-base manipulators. In order to illustrate this idea, we present a systematic method to obtain the singular solutions of a free-floating series-chain planar manipulator with revolute joints. We show that the singular configurations are solutions of simultaneous polynomial equations in the half-tangent of the joint variables. From the structure of these polynomial equations, we estimate the upper bound on the number of singularities of free-floating planar manipulators and compare these with analogous results for structurally similar fixed-base manipulators.

Over-Constrained Mechanisms Derived From RPRP Loops

2018 ◽  
Author(s):  
Kwun-Lon Ting ◽  
Kuan-Lun Hsu
Keyword(s):  
Computer Aided Design ◽  
Random Search ◽  
Modular Approach ◽  
Input Output ◽  
Assembly Strategy ◽  
Revolute Joints ◽  
Computer Aided ◽  
Prismatic Joints ◽  
Aided Design ◽  
Four Bar Linkage

This paper addresses the assembly strategy capable of deriving a family of over-constrained mechanisms systematically. The modular approach is proposed. It treats the topological synthesis of over-constrained mechanisms as a systematical derivation rather than a random search. The result indicates that a family of over-constrained mechanisms can be constructed by combining legitimate modules. A spatial four-bar linkage containing two revolute joints (R) and two prismatic joints (P) is selected as the source-module for the purpose of demonstration. All mechanisms discovered in this paper were modeled and animated with computer aided design (CAD) software and their mobility were validated with input-output equations as well as computer simulations. The assembly strategy can serve as a self-contained library of over-constrained mechanisms.

Overconstrained Mechanisms Derived From RPRP Loops

2018 ◽  
Vol 140 (6) ◽  
Author(s):  
Kuan-Lun Hsu ◽  
Kwun-Lon Ting
Keyword(s):  
Computer Aided Design ◽  
Random Search ◽  
Modular Approach ◽  
Input Output ◽  
Assembly Strategy ◽  
Revolute Joints ◽  
Prismatic Joints ◽  
Overconstrained Mechanisms ◽  
Aided Design ◽  
Four Bar Linkage

This paper addresses the assembly strategy capable of deriving a family of overconstrained mechanisms systematically. The modular approach is proposed. It treats the topological synthesis of overconstrained mechanisms as a systematical derivation rather than a random search. The result indicates that a family of overconstrained mechanisms can be constructed by combining legitimate modules. A spatial four-bar linkage containing two revolute joints (R) and two prismatic joints (P) is selected as the source-module for the purpose of demonstration. All mechanisms discovered in this paper were modeled and animated with computer-aided design (CAD) software and their mobility were validated with input–output equations as well as computer simulations. The assembly strategy can serve as a self-contained library of overconstrained mechanisms.

scholarly journals Dynamic Responses of Planar Multilink Mechanism considering Mixed Clearances

2020 ◽  
Vol 2020 ◽  
pp. 1-18
Author(s):  
Xiulong Chen ◽  
Shuai Jiang ◽  
Yu Deng
Keyword(s):  
Great Influence ◽  
Friction Model ◽  
Contact Forces ◽  
Dynamic Responses ◽  
Prototype Model ◽  
Planar Mechanisms ◽  
Coulomb’S Friction ◽  
Revolute Joints ◽  
Friction Models ◽  
Coulomb Friction Model

Translational and revolute joints are the main kinds of joints in planar multilink mechanisms. Translational and revolute clearance joints have great influence on dynamical responses of planar mechanisms. Most research studies mainly focused upon revolute clearance of planar mechanisms based upon the modified Coulomb friction model, some studies investigated clearance of the pin-slot joint, and few studies researched mixed clearances (considering both translational clearance and revolute clearance) based on the LuGre friction model. Dynamic response of the 2-DOF nine-bar mechanism considering mixed clearances based on the LuGre model is investigated in this work. The dynamic model with mixed clearances is built by the Lagrange multipliers. Dynamic responses including motion output of the slider, driving torques, contact forces, shaft center trajectories at revolute clearance pairs, and slider trajectory inside the guide are analyzed, respectively. Influences of different friction models on dynamic responses are studied, such as LuGre and modified Coulomb’s friction models. Effects of different clearance values and different driving speeds on dynamic responses with mixed clearances are both analyzed. Virtual prototype model considering mixed clearances is carried out through ADAMS to verify correctness.

Indentification and Classification of Multi-Degree-of-Freedom and Multi-Loop Mechanisms

1992 ◽  
Author(s):  
Tyng Liu ◽  
Chung-Huang Yu
Keyword(s):  
Industrial Applications ◽  
Degree Of Freedom ◽  
Constrained Motion ◽  
Structural Synthesis ◽  
Planar Mechanisms ◽  
Systematic Method ◽  
Revolute Joints ◽  
Systematic Scheme ◽  
Actual Degree

Abstract This study concerns the degree-of-freedom, the arrangements of input and the type of mobility of multi-loop, multi-degree-of-freedom mechanisms. Firstly, “basic loops” is introduced, and a systematic scheme for identifying the actual degree-of-freedom of mechanisms is developed. The input, then, can be properly deployed, such that the mechanism has a totally constrained motion. Lastly, based on the input deployment, the mobility of mechanisms is classifed and identified into three types: total, partial and fractionated mobility. The procedure has been automated, and the atlas of all possible arrangements of input of up to eight-link planar mechanisms with only revolute joints is presented. The systematic method is helpful for the structural synthesis of multi-degree-of-freedom and multi-loop mechanisms, and for exploring their potential industrial applications.

scholarly journals Numerical Synthesis of Six-Bar Linkages for Mechanical Computation

2014 ◽  
Vol 6 (3) ◽  
Author(s):  
Mark M. Plecnik ◽  
J. Michael McCarthy
Keyword(s):  
Parallel Computation ◽  
Design Procedure ◽  
Polynomial Equations ◽  
Output Function ◽  
Logarithmic Function ◽  
Input Output ◽  
Function Generator ◽  
Kinematic Synthesis ◽  
Isotropic Coordinates ◽  
Polynomial Degree

This paper presents a design procedure for six-bar linkages that use eight accuracy points to approximate a specified input–output function. In the kinematic synthesis of linkages, this is known as the synthesis of a function generator to perform mechanical computation. Our formulation uses isotropic coordinates to define the loop equations of the Watt II, Stephenson II, and Stephenson III six-bar linkages. The result is 22 polynomial equations in 22 unknowns that are solved using the polynomial homotopy software Bertini. The bilinear structure of the system yields a polynomial degree of 705,432. Our first run of Bertini generated 92,736 nonsingular solutions, which were used as the basis of a parameter homotopy solution. The algorithm was tested on the design of the Watt II logarithmic function generator patented by Svoboda in 1944. Our algorithm yielded his linkage and 64 others in 129 min of parallel computation on a Mac Pro with 12 × 2.93 GHz processors. Three additional examples are provided as well.

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