Dynamics of Chains of Rigid Bodies and Elastic Rods with Revolute and Prismatic Joints

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.

Download Full-text

Elastic rods, rigid bodies, quaternions and the last quadrature

Philosophical Transactions of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rsta.1997.0113 ◽

1997 ◽

Vol 355 (1732) ◽

pp. 2117-2136 ◽

Cited By ~ 47

Author(s):

S. Kehrbaum ◽

J. H. Maddocks

Keyword(s):

Rigid Bodies ◽

Elastic Rods

Download Full-text

Instantaneous Properties of Multi-Degrees-of-Freedom Motions—Point Trajectories

Journal of Mechanisms Transmissions and Automation in Design ◽

10.1115/1.3258773 ◽

1987 ◽

Vol 109 (1) ◽

pp. 107-115 ◽

Cited By ~ 13

Author(s):

Ashitava Ghosal ◽

Bernard Roth

Keyword(s):

General Framework ◽

Degrees Of Freedom ◽

Rigid Bodies ◽

Global Motion ◽

Analysis Techniques ◽

Trajectory Point ◽

Prismatic Joints ◽

Point Trajectories ◽

Three Degrees Of Freedom

A general framework is presented for the study of the properties of trajectories generated by points embedded in rigid bodies undergoing multi-degrees-of-freedom motions. Quantities are developed to characterize point trajectories generated by different mechanisms and to distinguish between different positions along the same trajectory. Point trajectories are classified into three types according to whether the number of degrees of freedom is less than, equal to, or greater than the dimension of the space in which the motion takes place. Local and global motion properties are developed for each of these three cases. A new way of using the redundant degrees of freedom in (redundant) mechanisms is presented. These analysis techniques are applied to two- and three-degrees-of-freedom mechanisms containing rotary and prismatic joints.

Download Full-text

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

Volume 6: 35th Mechanisms and Robotics Conference, Parts A and B ◽

10.1115/detc2011-47657 ◽

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.

Download Full-text

Modeling of a light elastic beam by a system of rigid bodies

Theoretical and Applied Mechanics ◽

10.2298/tam0404395s ◽

2004 ◽

Vol 31 (3-4) ◽

pp. 395-410 ◽

Cited By ~ 1

Author(s):

Slavisa Salinic

Keyword(s):

Potential Energy ◽

Stiffness Matrix ◽

Equations Of Motion ◽

Elastic Beam ◽

Kinematic Chain ◽

Vertical Axis ◽

Rigid Bodies ◽

Elastic Displacement ◽

Stiffness Matrices ◽

Prismatic Joints

This paper has shown that a light elastic beam, in the case of small elastic deformations, can be modeled by a kinematic chain without branching composed of rigid bodies which are connected by passive revolute or prismatic joints with corresponding springs in them. Elastic properties of the beam are modeled by the springs introduced. The potential energy of the elastic beam is expressed as a function of components of the vector of elastic displacement and the vector of elastic rotation calculated for the elastic centre of the beam, which results in the diagonal stiffness matrix of the beam. As the potential energy of the introduced system of bodies with springs is expressed in the function of relative joint displacements, the diagonal stiffness matrix is obtained. In addition, these two stiffness matrices are equal. The modeling process has been demonstrated on the example of an elastic beam rotating about a fixed vertical axis, with a rigid body whose mass is considerably larger than the beam mass fixed to its free end. Differential equations of motion have been formed for this mechanical system. The modeling technique described here aims at expanding of usage of well developed methods of dynamics of systems of rigid bodies to the analysis of systems with elastic bodies. .

Download Full-text

Singularity Traces of Planar Linkages That Include Prismatic and Revolute Joints

Volume 5B: 39th Mechanisms and Robotics Conference ◽

10.1115/detc2015-47390 ◽

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.

Download Full-text