A novel motion synthesis approach with expandable solution space for planar linkages based on kinematic-mapping

2016 ◽  
Vol 105 ◽  
pp. 164-175 ◽  
Author(s):  
Ping Zhao ◽  
Xiangyun Li ◽  
Lihong Zhu ◽  
Bin Zi ◽  
Q.J. Ge
Keyword(s):  
Solution Space ◽  
Motion Synthesis ◽  
Kinematic Mapping ◽  
Planar Linkages ◽  
Synthesis Approach

A Flexible Discrete Building Block Synthesis Approach As Basis for the Design of Planar Linkages

2017 ◽  
Author(s):  
Simon Laudahn ◽  
Franz Irlinger ◽  
Kassim Abdul-Sater
Keyword(s):  
Building Block ◽  
Integrated Design ◽  
Optimal Solution ◽  
Design Tool ◽  
Grid Search ◽  
Approximate Synthesis ◽  
Synthesis Procedure ◽  
Block Based ◽  
Planar Linkages ◽  
Synthesis Approach

In this paper we present a computational approximate synthesis procedure for the planar RR chain. Our approach is based on a grid search and takes an arbitrary amount of user-defined task positions for the two outer bodies of the chain and restrictions for both joints into account. The result of this synthesis approach is not only one optimal solution, but a list of several possible solutions which are ranked according to their performance. The approach aims at being used in building block-based synthesis procedures of more complex linkages. The method shall later be included into a CAD-integrated design tool for planar linkages.

scholarly journals Stable haptic feedback generation for mid-air gesture interactions: a hidden Markov model-based motion synthesis approach

2019 ◽  
Vol 6 (1) ◽  
Author(s):  
Dennis Babu ◽  
Masashi Konyo ◽  
Hikaru Nagano ◽  
Ryunosuke Hamada ◽  
Satoshi Tadokoro
Keyword(s):  
Markov Model ◽  
Hidden Markov Model ◽  
Haptic Feedback ◽  
Hidden Markov ◽  
Motion Synthesis ◽  
Model Based ◽  
Synthesis Approach

Design of Planar 1-DOF Cam-Linkages for Lower-Limb Rehabilitation Via Kinematic-Mapping Motion Synthesis Framework

2019 ◽  
Vol 11 (4) ◽  
Author(s):  
Ping Zhao ◽  
Lihong Zhu ◽  
Bin Zi ◽  
Xiangyun Li
Keyword(s):  
Lower Limb ◽  
Large Deviation ◽  
Motion Synthesis ◽  
Kinematic Constraint ◽  
Walking Motion ◽  
Kinematic Mapping ◽  
Limb Rehabilitation ◽  
The Given ◽  
Additional Constraints ◽  
Lower Limb Rehabilitation

When designing linkage mechanisms for motion synthesis, many examples have shown that the optimal kinematic constraint on the task motion contains too large deviation to be approximately viewed as a single rotational or translational pair. In this paper, we seek to adopt our previously established motion synthesis framework for the design of cam-linkages for a more accurate realization, while still maintaining a 1-degree-of-freedom (DOF) mechanism. To determine a feasible cam to lead through the task motion, first a kinematic constraint is identified such that a moving point on the given motion traces a curve that is algebraically closest to a circle or a line. This leads to a cam with low-harmonic contour curve that is simple and smooth to avoid the drawbacks of cam mechanisms. Additional constraints could also be imposed to specify the location and/or size of the cam linkages. An example of the design of a lower-limb rehabilitation device has been presented at the end of this paper to illustrate the feasibility of our approach. It is shown that our design could lead the user through a normal walking motion.

Motion Synthesis of Mechanisms Using Constraint Manifolds

1994 ◽  
Author(s):  
Y. K. Wu ◽  
Ian S. Fischer
Keyword(s):  
Curve Fitting ◽  
Optimization Algorithms ◽  
Image Space ◽  
Motion Synthesis ◽  
Numerical Examples ◽  
Synthesis Of Mechanisms ◽  
Normal Distance ◽  
Kinematic Mapping

Abstract The motion synthesis of a mechanism is obtained by curve fitting the intersection of the constraint manifolds representing each leg of the linkage in an image space to points obtained by the kinematic mapping of the prescribed positions and orientations. The dimensions of the mechanism can be found by using optimization algorithms to minimize the normal distance between all the desired image points and image curve of the tracer frame. The theory is illustrated by numerical examples.

scholarly journals A Parametrization-Invariant Fourier Approach to Planar Linkage Synthesis for Path Generation

2017 ◽  
Vol 2017 ◽  
pp. 1-16 ◽  
Author(s):  
Xiangyun Li ◽  
Peng Chen
Keyword(s):  
Design Space ◽  
Fourier Descriptors ◽  
Path Generation ◽  
Arc Length ◽  
Efficient Synthesis ◽  
Practical Applications ◽  
Classic Problem ◽  
Fourier Theory ◽  
Planar Linkages ◽  
Synthesis Approach

This paper deals with the classic problem of the synthesis of planar linkages for path generation. Based on the Fourier theory, the task curve and the synthesized four-bar coupler curve are regarded as the same curve if their Fourier descriptors match. Using Fourier analysis, a curve must be given as a function of time, termed a parametrization. In practical applications, different parametrizations can be associated with the same task and coupler curve, respectively; however, these parametrizations are Fourier analyzed to different Fourier descriptors, thus resulting in the mismatch of the task and coupler curve. In this paper, we present a parametrization-invariant method to eliminate the influence of parametrization on the values of Fourier descriptors by unifying given parametrizations to the arc length parametrization; meanwhile, a new design space decoupling scheme is introduced to separate the shape, size, orientation, and location matching of the task and four-bar curve, which leads naturally to an efficient synthesis approach.

Incorporating Fixed-Point and -Line Constraints and Tolerance Based Synthesis in 4MDS

2015 ◽  
Author(s):  
Anurag Purwar ◽  
Saurabh Bhapkar ◽  
Q. J. Ge
Keyword(s):  
Theoretical Foundation ◽  
Geometric Constraints ◽  
Machine Design ◽  
Design Stage ◽  
Design System ◽  
Motion Synthesis ◽  
Kinematic Mapping ◽  
Line Tangent ◽  
Fixed Line ◽  
Best Fit

This paper presents implementation of fixed-pivots, ground-link line, and tolerance based motion synthesis in the 4MDS (Four-Bar Motion Design System). This is a continuation of the first work reported on 4MDS, which provides an interactive, graphical, and geometric constraint based mechanism design system for the exact- and approximate-motion synthesis problems. Theoretical foundation of the 4MDS is laid over a kinematic mapping based unified formulation of the geometric constraints (circle, fixed-line, line-tangent-to-a-circle) associated with the mechanical dyads (RR, PR, and RP) of a planar four-bar mechanism. An efficient algorithm extracts the geometric constraints of a given motion task and determines the best dyad types as well as their dimensions that best fit to the motion. Often, Mechanism designers need to impose additional geometric constraints, such as specification of location of fixed pivots or ground-link line. If synthesized mechanism suffers from branch, circuit, or order defect, they may also desire rectified solutions by allowing a tolerance to certain or all task positions. Such functions are crucial to a practitioner and much needed during the conceptual design stage of machine design process.

scholarly journals A Unified Approach to Exact and Approximate Motion Synthesis of Spherical Four-Bar Linkages Via Kinematic Mapping

2017 ◽  
Vol 10 (1) ◽  
Author(s):  
Xiangyun Li ◽  
Ping Zhao ◽  
Anurag Purwar ◽  
Q. J. Ge
Keyword(s):  
Null Space ◽  
Solution Space ◽  
Quadratic Equation ◽  
Image Space ◽  
Geometric Constraints ◽  
Design Parameters ◽  
Space Representation ◽  
Motion Synthesis ◽  
Four Bar Linkage ◽  
Spherical Motion

This paper studies the problem of spherical four-bar motion synthesis from the viewpoint of acquiring circular geometric constraints from a set of prescribed spherical poses. The proposed approach extends our planar four-bar linkage synthesis work to spherical case. Using the image space representation of spherical poses, a quadratic equation with ten linear homogeneous coefficients, which corresponds to a constraint manifold in the image space, can be obtained to represent a spherical RR dyad. Therefore, our approach to synthesizing a spherical four-bar linkage decomposes into two steps. First, find a pencil of general manifolds that best fit the task image points in the least-squares sense, which can be solved using singular value decomposition (SVD), and the singular vectors associated with the smallest singular values are used to form the null-space solution of the pencil of general manifolds; second, additional constraint equations on the resulting solution space are imposed to identify the general manifolds that are qualified to become the constraint manifolds, which can represent the spherical circular constraints and thus their corresponding spherical dyads. After the inverse computation that converts the coefficients of the constraint manifolds to the design parameters of spherical RR dyad, spherical four-bar linkages that best navigate through the set of task poses can be constructed by the obtained dyads. The result is a fast and efficient algorithm that extracts the geometric constraints associated with a spherical motion task, and leads naturally to a unified treatment for both exact and approximate spherical motion synthesis.

Unified Motion Synthesis of Spatial Seven-Bar Platform Mechanisms and Planar-Four Bar Mechanisms

2020 ◽  
Author(s):  
Shashank Sharma ◽  
Anurag Purwar
Keyword(s):  
Solution Space ◽  
New Method ◽  
Hard Problem ◽  
Motion Generation ◽  
Motion Synthesis ◽  
Mechanism Synthesis ◽  
Generation Algorithm ◽  
Planar Mechanism ◽  
Multiplicity Of Solutions ◽  
Unified Algorithm

Abstract A unified motion generation algorithm that combines Spatial and Planar mechanism synthesis has been a hard problem in kinematics. In this paper, we present a new method to generate planar RRRR mechanisms and spatial 5-SS mechanisms using a unified algorithm. For a generalized spatial pose problem where all the poses fall on a plane, we show that there exist 1-∞ plane constraint solutions and 3-∞ planar-spherical solution dyads. We also show that for a spatial five pose problem where all poses lie on a plane, there exists a 2-∞ solution space of spherical and planar constraints. This multiplicity of solutions are intelligently constrained to find up to four circle constraints representing planar four-bar mechanism. Finally, examples are presented testing the proposed algorithm and verified using results from past publications.

Synthesis of Planar, Shape-Changing Rigid Body Mechanisms Approximating Closed Curves

2007 ◽  
Author(s):  
Justin A. Persinger ◽  
James P. Schmiedeler ◽  
Andrew P. Murray
Keyword(s):  
Numerical Optimization ◽  
Shape Change ◽  
Closed Curves ◽  
Single Degree Of Freedom ◽  
Revolute Joints ◽  
Planar Shape ◽  
A Chain ◽  
Planar Linkages ◽  
Arc Lengths ◽  
Synthesis Approach

This paper presents a procedure to synthesize planar linkages, composed of rigid links and revolute joints, that are capable of approximating a shape change defined by a set of closed curves possessing similar arc lengths. The synthesis approach is more rigorous and more broadly applicable to dramatic changes between larger numbers of shapes than existing techniques that employ graphical methods. Link geometry is determined through an existing procedure, and those links are then joined together in a chain using numerical optimization to minimize the error in approximating the shape change. Binary links are added to this chain via a search of the design space such that actuated links can be driven monotonically to exact the shape change. The focus is single-degree-of-freedom (DOF) mechanisms that approximate closed curves, but the methodology is similarly applicable to generating mechanisms approximating sets of open curves and multi-DOF systems. The procedure is applied to synthesize an example mechanism that changes between circular, elliptical, and teardrop shapes as inspired by an aerodynamic flow field modification application.

A Motion Synthesis Approach to Solving Alt-Burmester Problem by Exploiting Fourier Descriptor Relationship Between Path and Orientation Data

2018 ◽  
Vol 11 (1) ◽  
Author(s):  
Shashank Sharma ◽  
Anurag Purwar ◽  
Q. Jeffrey Ge
Keyword(s):  
Closed Form ◽  
Fourier Descriptors ◽  
Fourier Descriptor ◽  
Dimensional Synthesis ◽  
Motion Synthesis ◽  
Orientation Data ◽  
Synthesis Algorithm ◽  
Generalized Framework ◽  
Synthesis Approach

This paper presents a generalized framework to solve m-pose, n-path-points mixed synthesis problems, known as the Alt-Burmester problems, using a task-driven motion synthesis approach. We aim to unify the path and motion synthesis problems into an approximate mixed synthesis framework. Fourier descriptors are used to establish a closed-form relationship between the path and orientation data. This relationship is then exploited to formulate mixed synthesis problems into pure motion synthesis ones. We use an efficient algebraic fitting based motion synthesis algorithm to enable simultaneous type and dimensional synthesis of planar four-bar linkages.

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