MotionGen: An iOS and Android App for Planar Four-Bar Motion Generation

2016 ◽  
Author(s):  
Anurag Purwar ◽  
Shrinath Deshpande ◽  
Q. J. Ge
Keyword(s):  
Rigid Bodies ◽  
Geometric Constraints ◽  
Motion Generation ◽  
Unified Framework ◽  
Approximate Synthesis ◽  
Unified Algorithm ◽  
Android App ◽  
Google Android ◽  
High Utility ◽  
Generation Problem

MotionGen is an indigenously developed app for Apple iOS and Google Android platforms to help mechanism designers solve planar four-bar motion generation problem. The app is a computer implementation of authors’ recent work in developing a unified framework for the synthesis and simulation of planar four-bar mechanisms for the motion generation problem. Simplicity, high-utility, and wide-spread adoption of planar four-bar linkages have made them one of the most studied topics in Kinematics leading to development of algorithms and theories that deal with path-, function-, and motion generation-problems. Yet to date, there have been no attempts to develop efficient computational algorithms amenable to real-time computation of both type and dimensions of planar four-bar mechanisms for a given motion. MotionGen solves this problem effectively by extracting the geometric constraints of a given motion to provide the best dyad-types as well as dimensions of a total of up to six four-bar linkages. The unified algorithm also admits additional practical constraints, such as imposition of fixed- and moving-pivot and -line locations along with mixed exact- and approximate-synthesis scenarios. In that regard, its synthesis capabilities set it apart from other softwares of its ilk. However, its simulation approach also departs from more traditional methods, which typically involves assembling four rigid bodies and then designating fixed and moving links. Instead, the MotionGen requires users to assemble only two of the geometric constraints of mechanical dyads for quick prototyping of planar four-bar linkages. The app is equipped with an intuitive graphical user interface that allows a fluid dialog with the user to facilitate rapid manipulation and visualization of linkages.

MotionGen: Interactive Design and Editing of Planar Four-Bar Motions for Generating Pose and Geometric Constraints

2017 ◽  
Vol 9 (2) ◽  
Author(s):  
Anurag Purwar ◽  
Shrinath Deshpande ◽  
Q. J. Ge
Keyword(s):  
Geometric Constraints ◽  
Dimensional Synthesis ◽  
Motion Generation ◽  
Unified Framework ◽  
Synthesis Algorithm ◽  
Approximate Synthesis ◽  
High Utility ◽  
High Level ◽  
Generation Problem ◽  
Practical Constraints

In this paper, we have presented a unified framework for generating planar four-bar motions for a combination of poses and practical geometric constraints and its implementation in MotionGen app for Apple's iOS and Google's Android platforms. The framework is based on a unified type- and dimensional-synthesis algorithm for planar four-bar linkages for the motion-generation problem. Simplicity, high-utility, and wide-spread adoption of planar four-bar linkages have made them one of the most studied topics in kinematics leading to development of algorithms and theories that deal with path, function, and motion generation problems. Yet to date, there have been no attempts to develop efficient computational algorithms amenable to real-time computation of both type and dimensions of planar four-bar mechanisms for a given motion. MotionGen solves this problem in an intuitive fashion while providing high-level, rich options to enforce practical constraints. It is done effectively by extracting the geometric constraints of a given motion to provide the best dyad types as well as dimensions of a total of up to six four-bar linkages. The unified framework also admits a plurality of practical geometric constraints, such as imposition of fixed and moving pivot and line locations along with mixed exact and approximate synthesis scenarios.

Finite Position Synthesis of 5-SS Platform Linkages Including Partially Specified Joint Locations

2017 ◽  
Author(s):  
Xin Ge ◽  
Anurag Purwar ◽  
Q. J. Ge
Keyword(s):  
Linear Structure ◽  
Motion Generation ◽  
Numerical Examples ◽  
Moving Points ◽  
Unified Algorithm ◽  
Moving Platform ◽  
Position Synthesis ◽  
Partial Specification ◽  
Generation Problem ◽  
Novel Algorithm

A 5-SS platform linkage generates a one-degree-of-freedom motion of a moving platform such that each of five moving points on the platform is constrained on a sphere, or in its degenerated case, on a plane. It has been well established a 5-SS platform linkage can be made to guide though seven positions exactly. This paper investigates the cases when the number of given positions are less than seven that allows for partial specification of locations of the moving points. A recently developed novel algorithm with linear structure in the design equations has been extended for the solution of the problem. The formulation of this expanded motion generation problem unifies the treatment of the input positions and constraints on the moving and fixed joints associated with the 5-SS platform linkage. Numerical examples are provided to show the effectiveness of the unified algorithm.

A Task-Driven Approach to Optimal Synthesis of Planar Four-Bar Linkages for Extended Burmester Problem

2017 ◽  
Author(s):  
Shrinath Deshpande ◽  
Anurag Purwar
Keyword(s):  
Linear Constraints ◽  
Image Space ◽  
Geometric Constraints ◽  
Motion Generation ◽  
Quadratic Constraints ◽  
Special Cases ◽  
Non Linear ◽  
Approximate Synthesis ◽  
Step Algorithm ◽  
Value Decomposition

The classic Burmester problem is concerned with computing dimensions of planar four-bar linkages consisting of all revolute joints for five-pose problems. In the context of motion generation, each pose can be seen as a constraint that the coupler of a planar four-bar mechanism needs to interpolate or approximate through. We define extended Burmester problem as the one where all types of planar four-bars consisting of dyads of type RR, PR, RP, or PP (R: revolute, P: prismatic) and their dimensions need to be computed for n-geometric-constraints, where a geometric constraint can be an algebraically expressed constraint on the pose, or location of the fixed or moving pivots or something equivalent. In addition, we include both linear and non-linear and exact and approximate constraints. This extension also includes the problems where there is no solution to the classic Burmester problem, but designers would still like to design a four-bar that may come closest to capturing their intent. Such problems are representative of the problems that machine designers grapple with while designing linkage systems for a variety of constraints, which are not merely a set of poses. Recently, we have derived a unified form of geometric constraints of all types of dyads (RR, RP, PR, and PP) in the framework of kinematic mapping and planar quaternions, which map to generalized manifolds (G-manifolds) in the image space of planar displacements. The given poses map to points in the image space. Thus, the problem of synthesis is reduced to minimizing the algebraic error of fitting between the image points and the G-manifolds. We have also created a simple, two-step algorithm using Singular Value Decomposition (SVD) for the least-squares fitting of the manifolds, which yields a candidate space of solution. By imposing two fundamental quadratic constraints on the candidate solutions, we are able to simultaneously determine both the type and dimensions of the planar four-bar linkages. In this paper, we present 1) a unified approach for solving the extended Burmester problem by showing that all linear- and non-linear constraints can be handled in a unified way without resorting to special cases, 2) in the event of no or unsatisfactory solutions to the synthesis problem certain constraints can be relaxed, and 3) such constraints can be approximately satisfied by minimizing the algebraic fitting error using Lagrange Multiplier method. In doing so, we generalize our earlier formulation and present a new algorithm, which solves new problems including optimal approximate synthesis of Burmester problem with no exact solutions.

scholarly journals Euclidean metrics for motion generation on SE(3)

2002 ◽  
Vol 216 (1) ◽  
pp. 47-60 ◽  
Author(s):  
C Belta ◽  
V Kumar
Keyword(s):  
Ad Hoc ◽  
Trajectory Generation ◽  
Rigid Bodies ◽  
Second Step ◽  
Computationally Efficient ◽  
Motion Generation ◽  
Euclidean Group ◽  
Screw Motions ◽  
Euclidean Metrics ◽  
Generation Problem

Previous approaches to trajectory generation for rigid bodies have been either based on the so-called invariant screw motions or on ad hoc decompositions into rotations and translations. This paper formulates the trajectory generation problem in the framework of Lie groups and Riemannian geometry. The goal is to determine optimal curves joining given points with appropriate boundary conditions on the Euclidean group. Since this results in a two-point boundary value problem that has to be solved iteratively, a computationally efficient, analytical method that generates near-optimal trajectories is derived. The method consists of two steps. The first step involves generating the optimal trajectory in an ambient space, while the second step is used to project this trajectory onto the Euclidean group. The paper describes the method, its applications and its performance in terms of optimality and efficiency.

Optimal and Conforming Motion of a Point in a Constrained Plane

1989 ◽  
Author(s):  
C. Ahrikencheikh ◽  
A. A. Seireg ◽  
B. Ravani
Keyword(s):  
Free Space ◽  
Time Complexity ◽  
Velocity Vector ◽  
Automatic Generation ◽  
Geometric Constraints ◽  
Computational Time ◽  
Motion Generation ◽  
Optimal Point ◽  
Generation Algorithm

Abstract This paper deals with automatic generation of motion of a point under both geometric and non-geometric constraints. Optimal point paths are generated which are not only free of collisions with polygonal obstacles representing geometric constraints but also conform to non-geometric constraints such as speed of the motion, a maximum allowable change in the velocity vector and a minimum clearance from the obstacle boundaries. The concept of passage networks and conforming paths on the network are introduced. These are used to provide a new representation of the free space as well as a motion generation algorithm with a computational time complexity of only O(n3.log(n)), where n designates the total number of obstacle vertices. The algorithm finds the shortest or fastest (curved) path that also conforms with preset constraints on the motion of the point. The point paths generated are proved to be optimal while conforming to the constraints.

A Task Driven Approach to the Synthesis of Spherical 4R Linkages Using Algebraic Fitting Method

2013 ◽  
Author(s):  
Ping Zhao ◽  
Xiangyun Li ◽  
Anurag Purwar ◽  
Kartik Thakkar ◽  
Q. J. Ge
Keyword(s):  
Linear Method ◽  
Geometric Constraints ◽  
Motion Generation ◽  
Constraint Manifold ◽  
Fitting Method ◽  
Kinematic Mapping ◽  
Motion Approximation ◽  
The Given ◽  
Best Fit ◽  
Additional Constraints

This paper studies the problem of spherical 4R motion approximation from the viewpoint of extraction of circular geometric constraints from a given set of spherical displacements. This paper extends our planar 4R linkage synthesis work to the spherical case. By utilizing kinematic mapping and quaternions, we map spherical displacements into points and the workspace constraints of the coupler into intersection of algebraic quadrics (called constraint manifold), respectively, in the image space of displacements. The problem of synthesizing a spherical 4R linkage is reduced to finding a pencil of quadrics that best fit the given image points in the least squares sense. Additional constraints on the pencil identify the quadrics that represent a spherical circular constraint. The geometric parameters of the quadrics encode information about the linkage parameters which are readily computed to obtain a spherical 4R linkage that best navigates through the given displacements. The result is an efficient and largely linear method for spherical four-bar motion generation problem.

Elimination of Branch, Grashof, and Order Defects in Path-Angle Generation and Function Generation Synthesis

1979 ◽  
Vol 101 (3) ◽  
pp. 428-437 ◽  
Author(s):  
K. J. Waldron ◽  
E. N. Stevensen
Keyword(s):  
Motion Generation ◽  
Function Generation ◽  
And Function ◽  
Generation Problem

Path-Angle Generation and Function Generation synthesis problems are restated as Plane-Position (or Motion Generation) problems, enabling the use of the classical Burmester technique and recent extensions that permit the avoidance of Branch, Grashof, and Order defects. An example of the solution of a Path-Angle Generation problem is given.

A Unified Framework for Dynamics and Lyapunov Stability of Holonomically Constrained Rigid Bodies

2005 ◽  
Vol 9 (4) ◽  
pp. 387-394 ◽  
Author(s):  
Khoder Melhem ◽  
◽  
Zhaoheng Liu ◽  
Antonio Loría ◽  
◽  
...  
Keyword(s):  
System Dynamics ◽  
Lyapunov Stability ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Rigid Bodies ◽  
Minimal Realization ◽  
State Variables ◽  
Unified Framework ◽  
Constrained System ◽  
And Control

A new dynamic model for interconnected rigid bodies is proposed here. The model formulation makes it possible to treat any physical system with finite number of degrees of freedom in a unified framework. This new model is a nonminimal realization of the system dynamics since it contains more state variables than is needed. A useful discussion shows how the dimension of the state of this model can be reduced by eliminating the redundancy in the equations of motion, thus obtaining the minimal realization of the system dynamics. With this formulation, we can for the first time explicitly determine the equations of the constraints between the elements of the mechanical system corresponding to the interconnected rigid bodies in question. One of the advantages coming with this model is that we can use it to demonstrate that Lyapunov stability and control structure for the constrained system can be deducted by projection in the submanifold of movement from appropriate Lyapunov stability and stabilizing control of the corresponding unconstrained system. This procedure is tested by some simulations using the model of two-link planar robot.

A Task Driven Approach to Unified Synthesis of Planar Four-Bar Linkages Using Algebraic Fitting of a Pencil of G-Manifolds

2013 ◽  
Author(s):  
Q. J. Ge ◽  
Ping Zhao ◽  
Anurag Purwar
Keyword(s):  
Least Squares ◽  
Singular Values ◽  
Geometric Constraints ◽  
Motion Generation ◽  
Motion Approximation ◽  
Value Decomposition ◽  
Four Bar Linkage ◽  
The Given ◽  
Best Fit ◽  
Additional Constraints

This paper studies the problem of planar four-bar motion approximation from the viewpoint of extraction of geometric constraints from a given set of planar displacements. Using the Image Space of planar displacements, we obtain a class of quadrics, called Generalized- or G-manifolds, with eight linear and homogeneous coefficients as a unified representation for constraint manifolds of all four types of planar dyads, RR, PR, and PR, and PP. Given a set of image points that represent planar displacements, the problem of synthesizing a planar four-bar linkage is reduced to finding a pencil of G-manifolds that best fit the image points in the least squares sense. This least squares problem is solved using Singular Value Decomposition. The linear coefficients associated with the smallest singular values are used to define a pencil of quadrics. Additional constraints on the linear coefficients are then imposed to obtain a planar four-bar linkage that best guides the coupler through the given displacements. The result is an efficient and linear algorithm that naturally extracts the geometric constraints of a motion and leads directly to the type and dimensions of a mechanism for motion generation.

scholarly journals A unified framework for inferring the multi-scale organization of chromatin domains from Hi-C

2019 ◽  
Author(s):  
Ji Hyun Bak ◽  
Min Hyeok Kim ◽  
Lei Liu ◽  
Changbong Hyeon
Keyword(s):  
Statistical Physics ◽  
Building Blocks ◽  
Cell Types ◽  
Unified Framework ◽  
Global Pattern ◽  
Chromatin Domains ◽  
Chromosome Conformation ◽  
Multi Scale ◽  
Unified Algorithm ◽  
Different Cell Types

AbstractIdentifying chromatin domains (CDs) from high-throughput chromosome conformation capture (Hi-C) data is currently a central problem in genome research. Here we present a unified algorithm, Multi-CD, which infers CDs at various genomic scales by leveraging the information from Hi-C. By integrating a model of the chromosome from polymer physics, statistical physics-based clustering analysis, and Bayesian inference, Multi-CD identifies the CDs that best represent the global pattern of correlation manifested in Hi-C. The multi-scale intra-chromosomal structures compared across different cell types allow us to glean the principles of chromatin organization: (i) Sub-TADs, TADs, and meta-TADs constitute a robust hierarchical structure. (ii) The assemblies of compartments and TAD-based domains are governed by different organizational principles. (iii) Sub-TADs are the common building blocks of chromosome architecture. CDs obtained from Multi-CD applied to Hi-C data enable a quantitative and comparative analysis of chromosome organization in different cell types, providing glimpses into structure-function relationship in genome.

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