scholarly journals Kinematic Synthesis of Planar, Shape-Changing Rigid Body Mechanisms for Design Profiles With Significant Differences in Arc Length

2011 ◽  
Author(s):  
Shamsul A. Shamsudin ◽  
Andrew P. Murray ◽  
David H. Myszka ◽  
James P. Schmiedeler
Keyword(s):  
Rigid Body ◽  
Shape Change ◽  
Rigid Bodies ◽  
Arc Length ◽  
Shape Variation ◽  
Planar Mechanisms ◽  
Revolute Joints ◽  
Prismatic Joints ◽  
Plane Shape ◽  
A Chain

This paper presents a kinematic procedure to synthesize planar mechanisms capable of approximating a shape change defined by a general set of curves. These “morphing curves”, referred to as design profiles, differ from each other by a combination of displacement in the plane, shape variation, and notable differences in arc length. Where previous rigid-body shape-change work focused on mechanisms composed of rigid links and revolute joints to approximate curves of roughly equal arc length, this work introduces prismatic joints into the mechanisms in order to produce the different desired arc lengths. A method is presented to inspect and compare the profiles so that the regions are best suited for prismatic joints can be identified. The result of this methodology is the creation of a chain of rigid bodies connected by revolute and prismatic joints that can approximate a set of design profiles.

DESIGN AND ANALYSIS OF RIGID-BODY SHAPE-CHANGE MECHANISM FOR AIRCRAFT WINGS

2015 ◽  
Vol 77 (21) ◽  
Author(s):  
Mohammad Hazrin Ismail ◽  
Shamsul Anuar Shamsudin ◽  
Mohd Nizam Sudin
Keyword(s):  
Shape Change ◽  
Rigid Bodies ◽  
Main Body ◽  
Programming Technique ◽  
High Lift ◽  
Airframe Noise ◽  
Aircraft Wings ◽  
Prismatic Joints ◽  
A Chain ◽  
Fixed End

Airframe noise reduction becomes a main interest among researchers who study the performance of aircrafts. The airframe noise can occur between the high-lift systems and main body of the airfoil. The proposed shape-changing airfoil is one of many ideas to reduce airframe noise by eliminating the gap between the main body and high-lift systems. This paper presents a new design of 30P30N airfoil, which converts the three-element airfoil (slat, main body and flap) into two-element airfoil (combination of slat and main body as an element and flap) by installing a shape-changing slat into the systems. This work applies a chain of rigid bodies connected by revolute and prismatic joints that are capable of approximating a shape change defined by a set of morphed slat design profiles. To achieve a single degree of freedom (DOF), a building-block approach is employed to mechanize the fixed-end shape-changing chain with the helped of Geometric Constraint Programming technique as an effective method to develop the mechanism. The conventional and shape-change 30P30N airfoils are compared to study the performances of airfoils with the velocity and angle of attack are constant.

Kinematic Synthesis of Planar, Shape-Changing Rigid-Body Mechanisms

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
Andrew P. Murray ◽  
James P. Schmiedeler ◽  
Brian M. Korte
Keyword(s):  
Rigid Body ◽  
Degrees Of Freedom ◽  
Shape Change ◽  
Piecewise Linear ◽  
Single Chain ◽  
Planar Mechanisms ◽  
Revolute Joints ◽  
Planar Shape ◽  
Rigid Body Displacement ◽  
Shape Changes

This paper presents a kinematic procedure to synthesize planar mechanisms, composed of rigid links and revolute joints, capable of approximating a shape change defined by a set of curves. These “morphing curves”, referred to as design profiles, differ from each other by a combination of rigid-body displacement and shape change. Design profiles are converted to piecewise linear curves, referred to as target profiles, that can be readily manipulated. In the segmentation phase, the geometry of rigid links that approximate the shapes of corresponding segments from each target profile is determined. In the mechanization phase, these rigid links are joined together at their end points with revolute joints to form a single chain. Dyads are then added to reduce the number of degrees of freedom (DOF’s) to any desired value, typically 1. The approach can be applied to any number of design profiles that can be approximated with any number of rigid links, which can then be used to construct a mechanism with any number of DOF’s. Naturally, greater difficulty is encountered for larger numbers of design profiles and/or links and for more dramatic changes in shape. The procedure is demonstrated with examples of single-DOF mechanisms approximating shape changes between two and three design profiles.

Kinematic Synthesis of Planar, Shape-Changing Rigid-Body Mechanisms With Prismatic Joints

2011 ◽  
Author(s):  
Kai Zhao ◽  
James P. Schmiedeler ◽  
Andrew P. Murray
Keyword(s):  
Rigid Body ◽  
Shape Change ◽  
Weighted Least Squares ◽  
Solution Space ◽  
Building Blocks ◽  
Optimization Method ◽  
Basic Block ◽  
Closed Curves ◽  
Revolute Joints ◽  
Prismatic Joints

This paper presents a procedure to synthesize planar rigid-body mechanisms, containing both prismatic and revolute joints, capable of approximating a shape change defined by a set of morphing curves in different positions. With the introduction of prismatic joints, the existing mechanization process needs to be revisited via a building-block approach. The basic block is the Assur group of class II, and the auxiliary block is a fourbar mechanism, crank slider or binary link. To approximate shape changes defined by both open and closed curves, a single degree-of-freedom (DOF) mechanism is generated by assembling these building blocks. In the case of a large number of morphing curves, a weighted least squares approach is applied to determine center point locations for revolute joints and sliding paths for prismatic joints in individual building blocks. Then, the building blocks are located in an assembly position to regenerate the morphing chain using a numerical optimization method. Because of the additional constraints associated with prismatic joints compared to revolute joints, the size of the solution space is reduced, so random searches of the design space to find solution mechanisms are ineffective. A genetic algorithm is employed here instead to find a group of viable designs within reasonable computational limits. The procedure is demonstrated with synthesis examples of two 1-DOF mechanisms, one approximating five open-curve profiles and the other four closed-curve profiles.

Singularity Traces of Planar Linkages That Include Prismatic and Revolute Joints

2015 ◽  
Author(s):  
Saleh M. Almestiri ◽  
David H. Myszka ◽  
Andrew P. Murray ◽  
Charles W. Wampler
Keyword(s):  
Shape Change ◽  
Rigid Bodies ◽  
Closed Curves ◽  
Revolute Joints ◽  
Prismatic Joints ◽  
Kinematic Position ◽  
Motion Characteristics ◽  
Forward Kinematic ◽  
Planar Linkages ◽  
General Method

This paper presents a general method to construct a singularity trace for single degree-of-freedom, closed-loop linkages that include prismatic, in addition to, revolute joints. The singularity trace has been introduced in the literature as a plot that reveals the gross motion characteristics of a linkage relative to a designated input joint and design parameter. Previously, singularity traces were restricted to mechanisms composed of only rigid bodies and revolute joints. The motion characteristics identified on the plot include changes in the number of solutions to the forward kinematic position analysis (geometric inversions), singularities, and changes in the number of branches. To illustrate the adaptation of the general method to include prismatic joints, basic slider-crank and inverted slider-crank linkages are explored. Singularity traces are then constructed for more complex Assur IV/3 linkages containing multiple prismatic joints. These Assur linkages are of interest as they form an architecture that is commonly used for mechanisms capable of approximating a shape change defined by a general set of closed curves.

Design of Planar, Shape-Changing Rigid-Body Mechanisms for Morphing Aircraft Wings

2012 ◽  
Vol 4 (4) ◽  
Author(s):  
Kai Zhao ◽  
James P. Schmiedeler ◽  
Andrew P. Murray
Keyword(s):  
Rigid Body ◽  
Shape Change ◽  
Solution Space ◽  
Closed Curve ◽  
Morphing Aircraft ◽  
Aircraft Wings ◽  
Revolute Joints ◽  
Multi Objective Genetic Algorithm ◽  
Prismatic Joints ◽  
Fixed End

This paper presents a procedure to synthesize planar rigid-body mechanisms, containing both prismatic and revolute joints, capable of approximating a shape change defined by a set of morphing curves in different positions. The existing mechanization process is extended specifically to enable the design of morphing aircraft wings. A portion of the closed-curve morphing chain that has minimal displacement is identified as the structural ground after the segmentation process. Because of the revolute joints placed at the endpoints of the ground section, the moving links of the fixed-end morphing chain need to be repositioned relative to each of the desired wing shapes so as to minimize the error in approximating them. With the introduction of prismatic joints, a building-block approach is employed to mechanize the fixed-end morphing chain. The blocks are located in an assembly position to generate a single degree-of-freedom (DOF) mechanism. Because of the additional constraints associated with prismatic joints compared to revolute joints, the size of the solution space is reduced, so random searches of the design space to find solution mechanisms are ineffective. A multi-objective genetic algorithm is employed instead to find a group of viable designs that tradeoff minimizing matching error with maximizing mechanical advantage. The procedure is demonstrated with a synthesis example of a 1-DOF mechanism approximating eight closed-curve wing profiles.

Synthesis of Planar, Shape-Changing Rigid-Body Mechanisms

2006 ◽  
Author(s):  
Brian M. Korte ◽  
Andrew P. Murray ◽  
James P. Schmiedeler
Keyword(s):  
Rigid Body ◽  
Degrees Of Freedom ◽  
Shape Change ◽  
Piecewise Linear ◽  
Single Chain ◽  
Open Chain ◽  
Revolute Joints ◽  
Planar Shape ◽  
Rigid Body Displacement ◽  
Planar Linkages

This paper presents a procedure to synthesize planar linkages, composed of rigid links and revolute joints, capable of approximating a shape change defined by a set of curves. These “morphing curves” differ from each other by a combination of rigid-body displacement and shape change. Rigid link geometry is determined through analysis of piecewise linear curves to achieve shape-change approximation, and increasing the number of links improves the approximation. A mechanism is determined through connecting the rigid links into a single chain and adding dyads to eliminate degrees of freedom. The procedure is applied to two open-chain examples.

Axis Motion Based System Calibration of an Automated Disassembly Work Cell

2000 ◽  
Author(s):  
Michael M. Bailey-Van Kuren
Keyword(s):  
Vision System ◽  
Kinematic Model ◽  
Image Data ◽  
Simple Relationship ◽  
Revolute Joints ◽  
Prismatic Joints ◽  
Homogeneous Transformation Matrix ◽  
Position And Orientation ◽  
A Chain ◽  
User Friendly

Abstract This paper presents an approach to calibrate a robotic cell consisting of a robot, a positioning table and a stereo vision system in an autonomous manner. The approach is designed to simplify the error relationships and parameter updates and thus eliminating the need for a large nonlinear search. The accumulation of error in the kinematic model is avoided by calibrating one joint at a time from the manipulator hand to the manipulator base. The error in the manipulator and sensor models are identified by using least squares estimates. The manipulator kinematic model is parameterized by the joint axes position and orientation instead of the Denavit-Hartenberg parameters. This approach leads to a more “user-friendly” interface to the calibration results. The model is derived using screw geometry, resulting in a simple relationship between the joint axis parameters and the path produced by moving a particular joint. The robot model provides an example of a chain of revolute joints while the positioning table provides an example of prismatic joints. Model simplifications result from each of these simplified motions. As with other methods, this formulation produces a four by four homogeneous transformation matrix which defines the motion of any point on the hand of the manipulator in terms of the sensed joint angles. It is shown that each camera can independently estimate the manipulators’ paths using the image data and distances along the path from the manipulator model. Error in position and orientation between the resulting two path estimates identify the relative error between the camera models. It is shown that a solution exists for any set of three or more points generated from one axis.

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.

Multi-rigid-body modeling and simulation of perimodiolar cochlear electrode arrays

2019 ◽  
Vol 233 (5) ◽  
pp. 483-496 ◽  
Author(s):  
Ruifeng Zhu ◽  
Jianjun Li ◽  
Zuo Wang ◽  
Yongzhen Wu ◽  
Binrui Wang ◽  
...  
Keyword(s):  
Rigid Body ◽  
Electrode Array ◽  
Rigid Bodies ◽  
Shape Variation ◽  
Electrode Arrays ◽  
Angle Variation ◽  
Fitting Method ◽  
Adams Simulation ◽  
Rigid Body Model ◽  
Rigid Model

This study presented a method that decomposes perimodiolar electrodes into multi-rigid bodies for the study on the shape variation of cochlear perimodiolar electrode. The coordinates of electrode array were obtained by capturing the shape varying image of the perimodiolar electrodes with the stylet extracted. Subsequently, the increment of the angle variation and the length of each link were obtained. Fourier compensation fitting method was developed using the three fitting methods to compare and analyze the increment of the angle variation of the perimodiolar electrode multi-rigid model. This can not only ensure that the initial angle of the joint is consistent with the actual angle of the perimodiolar electrode, but also fully reflect the varying trend of the joint angle of the multi-rigid model of the perimodiolar electrode. The simulation of the shape variation of the perimodiolar electrode multi-rigid-body model was performed using this method in the ADAMS simulation platform. According to the simulation results, the precise and continuous shape variation of perimodiolar electrodes can be obtained using this method.

Synthesis of Planar Rigid-Body Mechanisms Approximating Shape Changes Defined by Closed Curves

2009 ◽  
Vol 131 (7) ◽  
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 ◽  
A Chain ◽  
Planar Linkages ◽  
Arc Lengths ◽  
Synthesis Approach ◽  
Shape Changes

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. It specifically addresses the challenges of approximating closed curves, but the methodology is equally applicable to open curves. 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, forming a single-degree-of-freedom mechanism in which an actuated link can be driven monotonically to exact the shape change. 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.

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