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.

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.

A generalised approach for the modelling of articulated open chain planar linkages

Robotica ◽  
1997 ◽  
Vol 15 (5) ◽  
pp. 523-531 ◽  
Author(s):  
Sedat Baysec ◽  
John Rees Jones
Keyword(s):  
Physical Model ◽  
Degrees Of Freedom ◽  
Initial Position ◽  
Open Chain ◽  
Positioning Systems ◽  
Six Degrees Of Freedom ◽  
Lagrange Formulation ◽  
Revolute Joints ◽  
Planar Linkages ◽  
Joint Velocity

In this paper a model to cover all possible topologies of robot manipulators composed of prismatic and revolute joints is presented. For simplicity, only planar systems are considered, hence to provide plane positioning, systems handled are of three degrees of freedom. The physical model assumes three moving rigid links in articulation with one revolute and one prismatic joint between each link pair, forming a six degrees of freedom open chain linkage. Among each joint pair, one is real and the other fictitious. The real joint is arbitrarily actuated by an externally applied force or torque while the fictitious one is acted upon by an appropriately controlled force or torque as to keep that joint velocity zero, keeping fixed at its initial position. The physical model is accompanied by a mathematical model obtained by Lagrange formulation. This approach is called ‘The method of Fictititous Degrees of Freedom’.

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.

Efficient Hyper-Volumetric Contact Dynamic Modelling of the Foot Within Human Gait Simulations

2013 ◽  
Author(s):  
Mohammad Sharif Shourijeh ◽  
John McPhee
Keyword(s):  
Rigid Body ◽  
Degrees Of Freedom ◽  
Center Of Pressure ◽  
Dynamic Modelling ◽  
Contact Model ◽  
Human Gait ◽  
Revolute Joints ◽  
Interaction Modelling ◽  
Reaction Forces ◽  
Hind Foot

This study describes the development of a multi-body foot contact model consisting of spherical volumetric models for the surfaces of the foot. The developed model is two-dimensional, and consists of two segments, the hind-foot, mid-foot, and forefoot as one rigid body and the phalanges collectively as the second rigid body. The model has four degrees of freedom: ankle x, y, hind-foot orientation, and metatarsal joint angle. Both ankle and metatarsal joints are assumed to be revolute joints. Three different types of contact elements are targeted: Kelvin-Voigt, linear volumetric, and nonlinear volumetric. The models are kinematically driven at the ankle and the metatarsal joints, and simulated horizontal and vertical ground reaction forces as well as center of pressure location are compared against the measured quantities within a complete human gait cycle. The hyper-volumetric foot contact model was found to be a suitable choice for foot/ground interaction modelling within human gait simulations.

Designing Variable-Geometry Extrusion Dies That Utilize Planar Shape-Changing Rigid-Body Mechanisms

2015 ◽  
Author(s):  
Bingjue Li ◽  
Andrew P. Murray ◽  
David H. Myszka
Keyword(s):  
Rigid Body ◽  
Cross Sections ◽  
Synthesis Process ◽  
Variable Geometry ◽  
Extrusion Dies ◽  
Geometry Design ◽  
Revolute Joints ◽  
Planar Shape ◽  
Fixed Line ◽  
Synthesis Methodology

This paper presents a kinematic synthesis methodology for planar shape-changing rigid-body mechanisms that addresses constraints arising in the design of variable-geometry polymer extrusion dies. Such a die is capable of morphing its orifice in order to create extrusions of non-constant cross section. A variable-geometry shape-changing die problem is defined by a set of design profiles of different shapes and arc lengths, which approximate various cross sections of the extrusion. The primary advantage of the presented methodology is addressing the need for bodies in the mechanism formed by fusing links in the shape-changing portion of the chain. Previous methodologies included such fused links, but only at the end of the synthesis process where revolute joints were seen to be underutilized. A new method is needed to control, or even eliminate the use of revolute joints in the shape-changing chain of rigid links. The result of this new work is an iterative method which generates an optimized morphing chain to best match the design profiles while minimizing the number of prismatic and revolute joints needed to do so. The additional variable-geometry design constraints also require a generalization to the definition of fixed-end profiles previously proposed, also allowing chain ends to be defined by prismatic joints on a fixed line of slide. A virtual-chain method is also proposed to solve closure problems caused by the reduction in the number of revolute joints.

scholarly journals Point-joint coordinate formulation for the dynamic analysis of generalised planar linkages

2005 ◽  
Vol 46 (4) ◽  
pp. 575-589
Author(s):  
Hazem Ali Attia
Keyword(s):  
Rigid Body ◽  
Dynamic Analysis ◽  
Equations Of Motion ◽  
Translational Motion ◽  
Constraint Forces ◽  
Constrained System ◽  
Open Chain ◽  
Closed Chain ◽  
Efficient Integration ◽  
Planar Linkages

AbstractThis paper presents a two-step formulation for the dynamic analysis of generalised planar linkages. First, a rigid body is replaced by a dynamically equivalent constrained system of particles and Newton's second law is used to study the motion of the particles without introducing any rotational coordinates. The translational motion of the constrained particles represents the general motion of the rigid body both translationally and rotationally. The simplicity and the absence of any rotational coordinates from the final form of the equations of motion are considered the main advantages of this formulation. A velocity transformation is then used to transform the equations of motion to a reduced set in terms of selected relative joint variables. For an open-chain, this process automatically eliminates all of the non-working constraint forces and leads to efficient integration of the equations of motion. For a closed-chain, suitable joints should be cut and some cut-joint constraint equations should be included. An example of a closed-chain is used to demonstrate the generality and efficiency of the proposed method.

A method for the solution of the forward position problems of planar mechanisms with prismatic and revolute joints

2001 ◽  
Vol 216 (4) ◽  
pp. 395-407 ◽  
Author(s):  
A Hernández ◽  
V Petuya ◽  
E Amezua
Keyword(s):  
Iterative Method ◽  
Degrees Of Freedom ◽  
Linear Equations ◽  
Simulation Program ◽  
Planar Mechanisms ◽  
Revolute Joints ◽  
Iteration Sequence ◽  
Geometrical Concepts ◽  
Planar Linkages ◽  
Non Linear Equations

In this paper, a method to solve the forward position problems of planar linkages with prismatic and revolute joints is presented. These linkages can have any number of degrees of freedom. This method has been named the geometrical iterative method and is based on geometrical concepts. An iteration sequence that corresponds to the system of non-linear equations describing closure of the mechanism loops is defined. This sequence is applied in successive iterations to obtain the position of the mechanism. In order to achieve convergence, the iteration sequence must fulfil two fundamental conditions. A searching algorithm has been developed to obtain a useful iteration sequence. It is based on the use of hierarchical rules and criteria. The method has been implemented in a simulation program developed by the authors. Several illustrative examples are presented using representative linkages.

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.

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.

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.

Sign in / Sign up

Export Citation Format

Share Document