Characterization of Workspaces of Parallel Manipulators

1992 ◽  
Vol 114 (3) ◽  
pp. 368-375 ◽  
Author(s):  
V. Kumar
Keyword(s):  
Parallel Manipulators ◽  
Geometric Optimization ◽  
Reachable Workspace ◽  
Serial Chain ◽  
Kinematic Performance ◽  
Serial Chains ◽  
Manipulator Control ◽  
General Method

The workspaces and kinematic characterization of serial chain manipulator geometries and the geometric optimization have been studied extensively. Much less is known about workspaces for manipulation systems which possess several serial chains arranged in parallel. In this paper, two well known workspaces, the reachable workspace and the dexterous workspace, are investigated for parallel manipulators. A general method for obtaining these workspaces is presented. The existence of numerous special configurations in the workspace present problems in manipulator control. Therefore the controllably dexterous workspace is proposed as a useful measure of kinematic performance. The methodology of delineating the workspaces and its limitations are illustrated with examples.

Kinestatic Analysis of General Parallel Manipulators

1995 ◽  
Vol 117 (4) ◽  
pp. 601-606 ◽  
Author(s):  
Shou-Hung Ling ◽  
Ming Z. Huang
Keyword(s):  
Jacobian Matrix ◽  
General Procedure ◽  
Parallel Manipulators ◽  
General Context ◽  
Chain Geometry ◽  
Parallel Chain ◽  
Serial Chain ◽  
Systematic Formulation ◽  
Serial Chains

Robotic mechanisms in general can be of either serial-chain, parallel-chain, or hybrid (a combination of both parallel and serial chains) geometry. While it can be asserted that kinematic theories and techniques are well established for fully serial-chain manipulators, the same assertion cannot be made when it is considered in the general context. In this article, we present a general procedure for systematic formulation and characterization of the instantaneous kinematics for a robotic mechanism with a general parallel-chain geometry. A kinestatic approach based on screw system theory is adopted in this treatment. The resulting equation is a compact Jacobian matrix of the system which includes attributes from not only the active joints but also the passive constraints. An example has been provided to demonstrate the methodology as well as its theoretical feasibility.

Inverse Kinematics for Planar Parallel Manipulators

1997 ◽  
Author(s):  
Robert L. Williams ◽  
Brett H. Shelley
Keyword(s):  
Inverse Kinematics ◽  
Broad Class ◽  
Parallel Manipulators ◽  
End Effector ◽  
Serial Chain ◽  
Prismatic Joints ◽  
Inverse Solutions ◽  
Three Degree Of Freedom ◽  
Serial Chains ◽  
Planar Parallel Manipulators

Abstract This paper presents algebraic inverse position and velocity kinematics solutions for a broad class of three degree-of-freedom planar in-parallel-actuated manipulators. Given an end-effector pose and rate, all active and passive joint values and rates are calculated independently for each serial chain connecting the ground link to the end-effector link. The solutions are independent of joint actuation. Seven serial chains consisting of revolute and prismatic joints are identified and their inverse solutions presented. To reduce computations, inverse Jacobian matrices for overall manipulators are derived to give only actuated joint rates. This matrix yields conditions for invalid actuation schemes. Simulation examples are given.

Formulation of Unique Form of Screw Based Jacobian for Lower Mobility Parallel Manipulators

2010 ◽  
Vol 3 (1) ◽  
Author(s):  
Man Bok Hong ◽  
Yong Je Choi
Keyword(s):  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Unique Form ◽  
Kinematic Chains ◽  
Revolute Joints ◽  
Serial Chain ◽  
Velocity Relation ◽  
Lower Mobility ◽  
Serial Chains ◽  
Inverse Velocity

In this paper, the unique form of the screw based Jacobian is suggested for lower mobility parallel manipulators. Utilizing the concept of the reciprocal Jacobian, the forward statics relation for each of the serial kinematic chains of a parallel manipulator can be first obtained and then used to derive both the forward statics and the inverse velocity relations of the manipulator. The screw based Jacobian of a parallel manipulator can be formulated from the inverse velocity relation in such a way that it consists of the reciprocal Jacobians of the serial kinematic chains. Since any reciprocal Jacobian is unique to the corresponding serial chain, the suggested form of the screw based Jacobian is also determined uniquely to the lower mobility parallel manipulator. Two examples are given to illustrate the proposed method, one for the 3DOF parallel manipulator with three identical prismatic-revolute-spherical joints-serial chains and the other for the 4DOF parallel manipulator with nonidentical serial chains (two spherical-prismatic-spherical- and one revolute-revolute-prismatic-revolute joints-serial chains).

Mobility of Single-Loop Kinematic Mechanisms Under Differential Displacement

2010 ◽  
Vol 132 (4) ◽  
Author(s):  
Paul Milenkovic
Keyword(s):  
Degrees Of Freedom ◽  
Single Loop ◽  
Kinematic Chains ◽  
Lie Bracket ◽  
Numerical Characterization ◽  
Serial Chain ◽  
Kinematic Mechanisms ◽  
Serial Chains ◽  
Analysis Of Motion

Linear analysis of motion screws is a means for determining the mobility of a mechanism composed of the parallel combination of serial kinematic chains. Such a mechanism may have one or more degrees of freedom that vanish after a differential displacement from a reference posture. The Lie product, also called the Lie bracket, is known to give the derivative of a motion screw with respect to the displacement along an upstream screw in a serial chain. Serial chains having motion screws that are closed under the Lie product are known to retain their mobility after differential displacement. For a single-loop mechanism, which is composed of a pair of chains that are not closed under the Lie product, mobility is retained when the Lie closures of those chains are within the span of the union of motion screws of the two chains, a new result determined by applying the Baker–Campbell–Hausdorff expansion to the motion screws of the serial chain. When the Lie products have at most one dimension outside the union span, a second-order expression of mobility reduces to a quadratic form, allowing the numerical characterization of constraint singularities under that condition.

Preparation and Characterization of β-glucosidase Films for Stabilization and Handling in Dry Configurations

2020 ◽  
Vol 21 (8) ◽  
pp. 741-747
Author(s):  
Liguang Zhang ◽  
Yanan Shen ◽  
Wenjing Lu ◽  
Lengqiu Guo ◽  
Min Xiang ◽  
...  
Keyword(s):  
Tensile Strength ◽  
Protein Function ◽  
Protein Stabilization ◽  
Functional Protein ◽  
Elongation At Break ◽  
Gelatin Films ◽  
The Stability ◽  
And Function ◽  
General Method

Background: Although the stability of proteins is of significance to maintain protein function for therapeutical applications, this remains a challenge. Herein, a general method of preserving protein stability and function was developed using gelatin films. Method: Enzymes immobilized onto films composed of gelatin and Ethylene Glycol (EG) were developed to study their ability to stabilize proteins. As a model functional protein, β-glucosidase was selected. The tensile properties, microstructure, and crystallization behavior of the gelatin films were assessed. Result: Our results indicated that film configurations can preserve the activity of β-glucosidase under rigorous conditions (75% relative humidity and 37°C for 47 days). In both control films and films containing 1.8 % β-glucosidase, tensile strength increased with increased EG content, whilst the elongation at break increased initially, then decreased over time. The presence of β-glucosidase had a negligible influence on tensile strength and elongation at break. Scanning electron-microscopy (SEM) revealed that with increasing EG content or decreasing enzyme concentrations, a denser microstructure was observed. Conclusion: In conclusion, the dry film is a promising candidate to maintain protein stabilization and handling. The configuration is convenient and cheap, and thus applicable to protein storage and transportation processes in the future.

Stochastic inequalities for an overflow model

1987 ◽  
Vol 24 (3) ◽  
pp. 696-708 ◽  
Author(s):  
Arie Hordijk ◽  
Ad Ridder
Keyword(s):  
Failure Rate ◽  
Lower Bounds ◽  
Approximation Method ◽  
Queueing Networks ◽  
Upper And Lower Bounds ◽  
Phase Type ◽  
Phase Type Distributions ◽  
Decreasing Failure Rate ◽  
General Method

A general method to obtain insensitive upper and lower bounds for the stationary distribution of queueing networks is sketched. It is applied to an overflow model. The bounds are shown to be valid for service distributions with decreasing failure rate. A characterization of phase-type distributions with decreasing failure rate is given. An approximation method is proposed. The methods are illustrated with numerical results.

scholarly journals Workspace Delineation of Cable-Actuated Parallel Manipulators

2004 ◽  
Author(s):  
Ethan Stump ◽  
Vijay Kumar
Keyword(s):  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Extensive Literature ◽  
Reachable Workspace ◽  
Planar Parallel Manipulator ◽  
Analytic Expressions

While there is extensive literature available on parallel manipulators in general, there has been much less attention given to cable-driven parallel manipulators. In this paper, we address the problem of analyzing the reachable workspace using the tools of semi-definite programming. We build on earlier work [1, 2] done using similar techniques by deriving limiting conditions that allow us to compute analytic expressions for the boundary of the reachable workspace. We illustrate this computation for a planar parallel manipulator with four actuators.

The Persistence of Formalism: Towards a Situated Critique beyond the Classic Separation of Powers

2010 ◽  
Vol 3 (2) ◽  
Author(s):  
Jose R. Rodriguez
Keyword(s):  
Social Relations ◽  
Social Practice ◽  
Legal Theory ◽  
Separation Of Powers ◽  
Academic Research ◽  
The Social ◽  
Critical Legal Theory ◽  
Theory Of Law ◽  
General Method

Formalism persists everywhere despite 100 years of critical legal theory. The reasons for that are sociological and political and include the persistence of the separation of powers idea as a central concept for the theory of law. In Brazil, this phenomenon manifests itself acutely for two supplementary reasons: (1) the lack of a real differentiation between academic research and professional lawyering and (2) the influence of neo-liberal economic thought.The persistence of formalism is a serious problem for Brazilian development since it naturalizes the existing institutions and their related power positions, creating an obstacle to any project of development that proposes something new. It blocks the development of a critical and reflexive knowledge on institutions, shortening institutional imagination to projects that could transform Brazilian reality.The main objective of this article is to develop a critique of formalism useful both as a general method to criticize formalism and as a tool to criticize its Brazilian manifestation. It will be argued here that the critique of formalism fails when it is only theoretical. An efficient critique must also grasp the ideas and the social relations responsible to reproduce formalism as a conceptual idea that informs social practices.To do that, this article will first propose a characterization of Brazilian formalism that does not fit in the Formalism X Instrumentalism dichotomy and is more adequate to grasp how law rationality works in countries from the Continental Law tradition. Afterwards, it will identify the power positions and the respective ideologies responsible to reproduce formalism in Brazil, giving criticism a sociological basis. Finally, it will show that only a positive view of what law should be will able to overcome formalism, both as a philosophical idea and as a social practice. In its final part, a sketch of such a view will be presented.

Clifford Algebra Exponentials and Planar Linkage Synthesis Equations

2004 ◽  
Vol 127 (5) ◽  
pp. 931-940 ◽  
Author(s):  
Alba Perez ◽  
J. Michael McCarthy
Keyword(s):  
Clifford Algebra ◽  
Standard Form ◽  
Algebraic Manipulation ◽  
Algebraic Solution ◽  
Linkage Design ◽  
Serial Chain ◽  
The Matrix ◽  
Basic Equations ◽  
Serial Chains ◽  
Linkage Synthesis

This paper uses the exponential defined on a Clifford algebra of planar projective space to show that the “standard-form” design equations used for planar linkage synthesis are obtained directly from the relative kinematics equations of the chain. The relative kinematics equations of a serial chain appear in the matrix exponential formulation of the kinematics equations for a robot. We show that formulating these same equations using a Clifford algebra yields design equations that include the joint variables in a way that is convenient for algebraic manipulation. The result is a single formulation that yields the design equations for planar 2R dyads, 3R triads, and nR single degree-of-freedom coupled serial chains and facilitates the algebraic solution of these equations including the inverse kinematics of the chain. These results link the basic equations of planar linkage design to standard techniques in robotics.

The Ray Optimization Method for the Determination of Workspaces of Planar Parallel Manipulators of General Design

2000 ◽  
Author(s):  
A. M. Hay ◽  
J. A. Snyman
Keyword(s):  
Computer Code ◽  
Parallel Manipulators ◽  
Optimization Method ◽  
Optimization Approach ◽  
Arbitrary Geometry ◽  
Planar Manipulators ◽  
Planar Parallel Manipulator ◽  
Point Interior ◽  
General Method

Abstract An extension to a novel optimization approach for the determination of workspaces of planar manipulators is presented. This approach provides a general method for the determination of manipulator workspaces and has the advantage that it may easily be automated. The method consists of finding a suitable initial radiating point interior to the accessible output set of the manipulator, and then determining the points of intersection of a representative pencil of rays, emanating from this point, with the boundary of the accessible set. The points of intersection are determined by means of an optimization approach in which a dynamic constrained optimization algorithm is used. If any section of the workspace boundary cannot be determined due to non-convexity, then the missing section is mapped using a suitably chosen new radiating point. The method is illustrated by its application to a generally constrained planar parallel manipulator. The method has been implemented in a practical, interactive computer code that has been used to determine convex and non-convex workspaces of different parallel manipulators of arbitrary geometry.

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