Equilibrators for Planar Linkages

1993 ◽  
Vol 115 (3) ◽  
pp. 604-611 ◽  
Author(s):  
D. A. Streit ◽  
E. Shin
Keyword(s):  
Mathematical Description ◽  
Higher Order ◽  
Mathematical Basis ◽  
New Approach ◽  
Kinematic Chains ◽  
Revolute Joints ◽  
Design Choice ◽  
New Methodologies ◽  
Planar Linkages ◽  
Two Degree Of Freedom

This manuscript provides a mathematical basis for comparing the complexity of equilibrator methodologies, extends the applications of those methodologies, and develops new methodologies. Two methodologies exist for spring equilibration of two degree of freedom revolute joint planar linkages. Extensions of both methodologies are now demonstrated for equilibration of all rigid body planar linkages having lower and/or higher order kinematic pairs. Reduction in complexity of these general methodologies is demonstrated when kinematic chains include only revolute joints. A mathematical description of the complexity of each of three equilibration methodologies is introduced to provide a means of comparing the effectiveness of each approach. Examples demonstrate the appropriate equilibrator design choice for particular applications, based on the mathematical description of system complexity. A new approach for equilibration of linkages having higher order planar kinematic pairs (1R1T) is introduced. A solution to the problem of spring mass in equilibrator design is presented. Examples are included to demonstrate the effectiveness of both the 1R1T equilibrator design scheme, and the spring mass equilibration scheme. The 1R1T design represents a first equilibration of pantograph type mechanisms.

A new approach for studying vertical infiltration

Soil Research ◽  
2020 ◽  
Vol 58 (5) ◽  
pp. 509
Author(s):  
Alexander Poulovassilis ◽  
Ioannis Argyrokastritis
Keyword(s):  
Hydraulic Properties ◽  
Pressure Head ◽  
Gradient Term ◽  
Infiltration Process ◽  
New Approach ◽  
Homogeneous Porous Media ◽  
Cumulative Infiltration ◽  
Head Gradient ◽  
Cumulative Curve ◽  
New Methodologies

The exact contribution of the pressure head gradient term during the vertical infiltration process, occurring in homogeneous porous media under zero ponding head, is determined analytically to advance the knowledge related to the infiltration phenomenon. This contribution is smaller than that of the horizontal infiltration by a factor at which is a measurable function of the infiltration time t, characteristic of each porous body. By adding to this contribution that of gravity, a new two-term analytical equation is formulated which exactly reproduces an available vertical cumulative curve and satisfies the physics governing infiltration process. The properties of at allow the derivation of an equation accurate for small and moderate t and of another one accurate for all t, including large values. By applying new methodologies, the values of the sorptivity and hydraulic conductivity are determined analytically from an available cumulative infiltration curve. Philip’s two-term equation, which does not satisfy the physical requirements at the upper extreme of t, and three other equations that do satisfy it, are examined in the light of the findings of the present work. The proposed equations are able to describe the vertical infiltration process and may be used to provide the hydraulic properties.

scholarly journals IRSBot-2: A Novel Two-DOF Parallel Robot for High-Speed Operations

2011 ◽  
Author(s):  
Coralie Germain ◽  
Se´bastien Briot ◽  
Victor Glazunov ◽  
Ste´phane Caro ◽  
Philippe Wenger
Keyword(s):  
High Speed ◽  
Parallel Robot ◽  
Degree Of Freedom ◽  
Kinematic Chains ◽  
Robot Architecture ◽  
Intrinsic Stiffness ◽  
Two Degree Of Freedom

This paper presents a novel two-degree-of-freedom (DOF) translational parallel robot for high-speed applications named the IRSBot-2 (acronym for IRCCyN Spatial Robot with 2 DOF). Unlike most two-DOF robots dedicated to planar translational motions, this robot has two spatial kinematic chains which confers a very good intrinsic stiffness. First, the robot architecture is described. Then, its actuation and constraint singularities are analyzed. Finally, the IRSBot-2 is compared to its two-DOF counterparts based on elastostatic performances.

A New Approach for Locating the Instantaneous Centers of Zero Velocity for 1-DOF Planar Linkages

2018 ◽  
Author(s):  
Nadim Diab
Keyword(s):  
Degree Of Freedom ◽  
Planar Mechanisms ◽  
New Approach ◽  
Zero Velocity ◽  
Graphical Technique ◽  
Instantaneous Center ◽  
Planar Linkages ◽  
Consistent Approach

This paper presents a new graphical technique to locate the secondary instantaneous centers of zero velocity (ICs) for one-degree-of-freedom (1-DOF) kinematically indeterminate planar mechanisms. The proposed approach is based on transforming the 1-DOF mechanism into a 2-DOF counterpart by converting any ground-pivoted ternary link into two ground-pivoted binary links. Fixing each of these two new binary links, one at a time, results in two different 1-DOF mechanisms where the intersection of the loci of their instantaneous centers will determine the location of the desired instantaneous center for the original 1-DOF mechanism. This single and consistent approach proved to be successful in locating the ICs of various mechanisms reported in the literature that required different techniques to reach the same results obtained herein.

Analysis of Force Distribution in Grasps Using Augmentation

1996 ◽  
Vol 210 (1) ◽  
pp. 15-22 ◽  
Author(s):  
J S Dai ◽  
D R Kerr
Keyword(s):  
Rigid Body ◽  
Equilibrium Condition ◽  
Jacobian Matrix ◽  
Point Contact ◽  
Force Distribution ◽  
Mathematical Basis ◽  
New Approach ◽  
Contact Points ◽  
Geometric Compatibility ◽  
Force Equilibrium

A new approach to the analysis of statically indeterminate restraint of a rigid body with any arrangement of point contact is presented in this paper. The paper associates the elasticity at restraint contacts with geometric compatibility of the contact points and constructs elastic compatibility equations, which are complementary to the restraint equations. The equations so obtained are then used to augment the restraint equations and lead to an agumented Jacobian matrix. The new approach enables grasps to be analysed and synthesized in a constraint of combined elasticity and geometric compatibility, in addition to the force equilibrium condition. This gives a mathematical basis for the analysis of force distribution of the statically indeterminate restraint. Detailed reasoning and derivations are given followed by both planar and spatial examples.

Asymptotic analysis of the classical aircraft stability equations

1999 ◽  
Vol 103 (1020) ◽  
pp. 95-103 ◽  
Author(s):  
W. R. Graham
Keyword(s):  
Asymptotic Analysis ◽  
Natural Frequencies ◽  
A Priori ◽  
New Approach ◽  
Advanced Level ◽  
Analytical Approximations ◽  
Short Period ◽  
Period Oscillation ◽  
Dutch Roll ◽  
Two Degree Of Freedom

Abstract A new approach to deriving analytical approximations for the free modes of motion of an aircraft is presented. Based on an asymptotic analysis, it eliminates the need for a priori assumptions regarding the characteristic motion of each mode, and is thus particularly suitable for an introductory exposition. In its basic form, it yields expressions for natural frequencies, damping factors and time constants which agree, to leading order, with well established results. At a more advanced level, it allows us to assess the validity of these results. In particular, we find that the two degree-of-freedom approximations to the short period oscillation and Dutch roll are asymptotically incorrect. This is unlikely to have a significant effect on the accuracy of the former, but is the reason for the poor damping predictions of the latter.

On Asymptotic Approximations to a Class of Regular Perturbation Problems

1977 ◽  
Vol 99 (3) ◽  
pp. 369-375 ◽  
Author(s):  
D. A. MacDonald
Keyword(s):  
Algebraic Manipulation ◽  
Higher Order ◽  
Standard Theory ◽  
Asymptotic Approximations ◽  
Rounding Error ◽  
Common Occurrence ◽  
Regular Perturbation ◽  
New Approach ◽  
Exact Agreement ◽  
Perturbation Problems

A new approach to a class of regular perturbation problems of common occurrence in lubrication theory is presented. The approach is not dependent on extensive algebraic manipulation and predicts results which, apart from numerical rounding error, are in exact agreement with standard theory. Three illustrative examples are studied in detail and it is demonstrated that asymptotic approximations obtained through use of the approach can be of a substantially higher order than approximations at present in the literature.

Kinematic Synthesis of Minimally Actuated Multi-Loop Planar Linkages With Second Order Motion Constraints for Object Grasping

2013 ◽  
Author(s):  
Gim Song Soh ◽  
Nina Robson
Keyword(s):  
Second Order ◽  
Human Robot Interaction ◽  
Degree Of Freedom ◽  
Dimensional Synthesis ◽  
Open Problems ◽  
Kinematic Synthesis ◽  
Human Environment ◽  
Kinematic Chains ◽  
Curvature Effects ◽  
Planar Linkages

In this paper, we consider the dimensional synthesis of one degree-of-freedom multi-loop planar linkages such that they do not violate normal direction and second order curvature constraints imposed by contact with objects. Our goal is in developing minimally actuated multi-loop mechanical devices for human-robot interaction, that is, devices whose tasks will happen in a human environment. Currently no systematic method exists for the kinematic synthesis of robotic fingers that incorporate multi-loop kinematic structure with second order task constraints, related to curvature. We show how to use these contact and curvature effects to formulate the synthesis equations for the design of a planar one-degree-of-freedom six-bar linkage. An example for the design of a finger that maintains a specified contact with an object, for an anthropomorphic task, is presented at the end of the paper. It is important to note, that the theoretical foundation presented in this paper, assists in solving some of the open problems of this field, providing preliminary results on the synthesis of kinematic chains with multi-loop topology and the use of novel task specifications that incorporate curvature constraints with future applications in grasping and object manipulation.

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