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.

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.

Synthesis of Planar Mechanisms for Pick and Place Tasks With Guiding Locations

2013 ◽  
Author(s):  
Pierre Larochelle
Keyword(s):  
Algebraic Geometry ◽  
Constraint Equation ◽  
Dimensional Synthesis ◽  
Motion Generation ◽  
Planar Mechanisms ◽  
Open Chain ◽  
Synthesis Algorithm ◽  
Kinematic Chains ◽  
Synthesis Technique ◽  
Kinematic Inversion

A novel dimensional synthesis technique for solving the mixed exact and approximate motion synthesis problem for planar RR kinematic chains is presented. The methodology uses an analytic representation of the planar RR dyads rigid body constraint equation in combination with an algebraic geometry formulation of the exact synthesis for three prescribed locations to yield designs that exactly reach the prescribed pick & place locations while approximating an arbitrary number of guiding locations. The result is a dimensional synthesis technique for mixed exact and approximate motion generation for planar RR dyads. A solution dyad may be directly implemented as a 2R open chain or two solution dyads may be combined to form a planar 4R closed chain; also known as a planar four-bar mechanism. The synthesis algorithm utilizes only algebraic geometry and does not require the use of a numerical optimization algorithm or a metric on planar displacements. Two implementations of the synthesis algorithm are presented; computational and graphical construction. Moreover, the kinematic inversion of the algorithm is also included. An example that demonstrates the synthesis technique is included.

A Computational Geometric Approach for Motion Generation of Spatial Linkages With Sphere and Plane Constraints

2018 ◽  
Vol 11 (1) ◽  
Author(s):  
Xiangyun Li ◽  
Q. J. Ge ◽  
Feng Gao
Keyword(s):  
Geometric Approach ◽  
Geometric Constraints ◽  
Dimensional Synthesis ◽  
Motion Generation ◽  
Geometric Framework ◽  
Kinematic Chains ◽  
Kinematic Mapping ◽  
Spherical Linkages ◽  
Spatial Displacements ◽  
The Given

This paper studies the problem of spatial linkage synthesis for motion generation from the perspective of extracting geometric constraints from a set of specified spatial displacements. In previous work, we have developed a computational geometric framework for integrated type and dimensional synthesis of planar and spherical linkages, the main feature of which is to extract the mechanically realizable geometric constraints from task positions, and thus reduce the motion synthesis problem to that of identifying kinematic dyads and triads associated with the resulting geometric constraints. The proposed approach herein extends this data-driven paradigm to spatial cases, with the focus on acquiring the point-on-a-sphere and point-on-a-plane geometric constraints which are associated with those spatial kinematic chains commonly encountered in spatial mechanism design. Using the theory of kinematic mapping and dual quaternions, we develop a unified version of design equations that represents both types of geometric constraints, and present a simple and efficient algorithm for uncovering them from the given motion.

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.

Synthesis of Planar Mechanisms for Pick and Place Tasks With Guiding Positions

2015 ◽  
Vol 7 (3) ◽  
Author(s):  
Pierre Larochelle
Keyword(s):  
Algebraic Geometry ◽  
Constraint Equation ◽  
Dimensional Synthesis ◽  
Motion Generation ◽  
Open Chain ◽  
Synthesis Algorithm ◽  
Kinematic Chains ◽  
Synthesis Technique ◽  
Pick And Place ◽  
Kinematic Inversion

A novel dimensional synthesis technique for solving the mixed exact and approximate motion synthesis problem for planar RR kinematic chains is presented. The methodology uses an analytic representation of the planar RR dyad's rigid body constraint equation in combination with an algebraic geometry formulation of the exact synthesis for three prescribed positions to yield designs that exactly reach the prescribed pick and place positions while approximating an arbitrary number of guiding positions. The result is a dimensional synthesis technique for mixed exact and approximate motion generation for planar RR dyads. A solution dyad may be directly implemented as a 2R open chain or two solution dyads may be combined to form a planar 4R closed chain, also known as a planar four-bar mechanism. The synthesis algorithm utilizes only algebraic geometry and does not require the use of a numerical optimization algorithm or a metric on elements of SE(2); the group of planar displacements. Two implementations of the synthesis algorithm are presented; computational and graphical construction. Moreover, the kinematic inversion of the algorithm is also included. Two examples that demonstrate the synthesis technique are included.

Synthesis of Watt II Mechanisms for Four Simultaneous Positions

2015 ◽  
Author(s):  
Pierre Larochelle ◽  
Jugesh Sundram ◽  
Ronald A. Zimmerman
Keyword(s):  
Algebraic Geometry ◽  
Dimensional Synthesis ◽  
Motion Generation ◽  
Generation Task ◽  
Kinematic Synthesis ◽  
Synthesis Algorithm ◽  
Relative Angle ◽  
Synthesis Technique ◽  
Two Bodies

This article presents the kinematic synthesis of Watt II six-bar mechanisms for simultaneously guiding two bodies through four prescribed positions. The two bodies to be moved are connected by a revolute joint and the motion generation task is defined by the four desired positions of one body and the relative angle of the second body with respect to the first body. The methodology uses an algebraic geometry formulation of the exact synthesis of planar RR dyads for four prescribed positions from classical Burmester theory. The result is a dimensional synthesis technique for designing Watt II mechanisms for four simultaneous positions. A case study illustrating the application of the synthesis algorithm is included.

An Interactive Graphical Approach to Feature Modeling Using Halfspaces and Geometric Constraints

1990 ◽  
Author(s):  
Maarten J. G. M. van Emmerik
Keyword(s):  
Spatial Relations ◽  
Feature Modeling ◽  
Geometric Constraints ◽  
Boolean Combination ◽  
Graphical Approach ◽  
Geometric Characteristics ◽  
Feature Based ◽  
New Feature ◽  
High Level ◽  
And Control

Abstract Feature modeling enables the specification of a model with standardized high-level shape aspects that have a functional meaning for design or manufacturing. In this paper an interactive graphical approach to feature-based modeling is presented. The user can represent features as new CSG primitives, specified as a Boolean combination of halfspaces. Constraints between halfspaces specify the geometric characteristics of a feature and control feature validity. Once a new feature is defined and stored in a library, it can be used in other objects and positioned, oriented and dimensioned by direct manipulation with a graphics cursor. Constraints between features prevent feature interference and specify spatial relations between features.

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.

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