Stiffness of Cable-based Parallel Manipulators With Application to Stability Analysis

2005 ◽  
Vol 128 (1) ◽  
pp. 303-310 ◽  
Author(s):  
Saeed Behzadipour ◽  
Amir Khajepour
Keyword(s):  
Stability Analysis ◽  
Trajectory Planning ◽  
Stiffness Matrix ◽  
Sufficient Conditions ◽  
Parallel Manipulators ◽  
Rotational Stiffness ◽  
New Approach ◽  
Cable Forces

The stiffness of cable-based robots is studied in this paper. Since antagonistic forces are essential for the operation of cable-based manipulators, their effects on the stiffness should be considered in the design, control, and trajectory planning of these manipulators. This paper studies this issue and derives the conditions under which a cable-based manipulator may become unstable because of the antagonistic forces. For this purpose, a new approach is introduced to calculate the total stiffness matrix. This approach shows that, for a cable-based manipulator with all cables in tension, the root of instability is a rotational stiffness caused by the internal cable forces. A set of sufficient conditions are derived to ensure the manipulator is stabilizable meaning that it never becomes unstable upon increasing the antagonistic forces. Stabilizability of a planar cable-based manipulator is studied as an example to illustrate this approach.

Stiffness Analysis and Comparison of 3-PPR Planar Parallel Manipulators With Actuation Compliance

2012 ◽  
Author(s):  
Guanglei Wu ◽  
Shaoping Bai ◽  
Jørgen A. Kepler
Keyword(s):  
Stiffness Matrix ◽  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Graphic Representation ◽  
Rotational Stiffness ◽  
Stiffness Analysis ◽  
Planar Parallel Manipulator ◽  
Stiffness Characteristics ◽  
Planar Parallel Manipulators

In this paper, the stiffness of 3-PPR planar parallel manipulator (PPM) is analyzed with the consideration of nonlinear actuation compliance. The characteristics of the stiffness matrix pertaining to the planar parallel manipulators are analyzed and discussed. Graphic representation of the stiffness characteristics by means of translational and rotational stiffness mapping is developed. The developed method is illustrated with an unsymmetrical 3-PPR PPM, being compared with its structure-symmetrical counterpart.

Virtual-mechanism-based analysis of cooperative manipulation

2005 ◽  
Vol 219 (3) ◽  
pp. 315-323
Author(s):  
H Liu ◽  
J S Dai ◽  
H Y Xu ◽  
H Li
Keyword(s):  
Trajectory Planning ◽  
Manipulation Planning ◽  
End Points ◽  
New Approach ◽  
Cooperative Manipulation ◽  
Hypothetical Mechanism ◽  
End Effectors ◽  
Cooperative Manipulators ◽  
Mechanism Theory

This paper proposes a new approach for analysing cooperative manipulation in which cooperative manipulators form a mechanism closure that allows a virtual-mechanism-based analysis to take place. The method is based on the geometry of manipulators during manipulation and converts the cooperative manipulation problem into the analysis of a hypothetical mechanism so that the mechanism theory can be used for the manipulation. This mechanism is hence generated by the fact that the end points (or geometric centres of respective grippers) of cooperative manipulators coincide with a virtual joint during cooperative manipulation. The analysis not only generates positions and orientations of the end effectors of cooperative manipulators but also produces corresponding link configurations that can be used for manipulation planning. The approach is further used for the orientation-based trajectory planning with two different cases. Simulations and discussions are made with respect to cooperative manipulations using two 2R manipulators and one 2R manipulators and one 3R manipulator.

Structure Synthesis of 3-RRS Type Spatial Compliant Parallel Manipulator

2010 ◽  
Vol 44-47 ◽  
pp. 1375-1379
Author(s):  
Da Chang Zhu ◽  
Li Meng ◽  
Tao Jiang
Keyword(s):  
Parallel Manipulator ◽  
Compliant Mechanisms ◽  
Screw Theory ◽  
Weight Ratio ◽  
Parallel Manipulators ◽  
Robot System ◽  
New Approach ◽  
Structure Synthesis ◽  
Rigid Joints ◽  
Type 3

Parallel manipulators has been extensively studied by virtues or its high force-to-weight ratio and widely spread applications such as vehicle or flight simulator, a machine tool and the end effector of robot system. However, as each limb includes several rigid joints, assembling error is demanded strictly, especially in precision measurement and micro-electronics. On the other hand, compliant mechanisms take advantage of recoverable deformation to transfer or transform motion, force, or energy and the benefits of compliant mechanisms mainly come from the elimination of traditional rigid joints, but the traditional displacement method reduce the stiffness of spatial compliant parallel manipulators. In this paper, a new approach of structure synthesis of 3-DoF rotational compliant parallel manipulators is proposed. Based on screw theory, the structures of RRS type 3-DoF rotational spatial compliant parallel manipulator are developed. Experiments via ANSYS are conducted to give some validation of the theoretical analysis.

A new approach to the stability analysis of thawing slopes

1980 ◽  
Vol 17 (4) ◽  
pp. 607-612 ◽  
Author(s):  
Luis E. Vallejo
Keyword(s):  
Stability Analysis ◽  
Water Content ◽  
Pore Water ◽  
Active Layer ◽  
Necessary Conditions ◽  
Mass Movements ◽  
New Approach ◽  
Pore Water Pressures ◽  
The Stability ◽  
Excess Pore

A new approach to the stability analysis of thawing slopes at shallow depths, taking into consideration their structure (this being a mixture of hard crumbs of soil and a fluid matrix), is presented. The new approach explains shallow mass movements such as skin flows and tongues of bimodal flows, which usually take place on very low slope inclinations independently of excess pore water pressures or increased water content in the active layer, which are necessary conditions in the methods available to date to explain these movements.

scholarly journals Exponential Stability of Periodic Solution to Wilson-Cowan Networks with Time-Varying Delays on Time Scales

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Jinxiang Cai ◽  
Zhenkun Huang ◽  
Honghua Bin
Keyword(s):  
Periodic Solution ◽  
Stability Analysis ◽  
Exponential Stability ◽  
Time Scales ◽  
Continuous Time ◽  
Lyapunov Functional ◽  
Contraction Mapping ◽  
Sufficient Conditions ◽  
Contraction Mapping Principle ◽  
Time Varying

We present stability analysis of delayed Wilson-Cowan networks on time scales. By applying the theory of calculus on time scales, the contraction mapping principle, and Lyapunov functional, new sufficient conditions are obtained to ensure the existence and exponential stability of periodic solution to the considered system. The obtained results are general and can be applied to discrete-time or continuous-time Wilson-Cowan networks.

A Statically Balanced Gough/Stewart-Type Platform: Conception, Design, and Simulation

2009 ◽  
Vol 1 (3) ◽  
Author(s):  
Marco Carricato ◽  
Clément Gosselin
Keyword(s):  
Sufficient Conditions ◽  
Parallel Manipulators ◽  
Point Of View ◽  
Theoretical Point ◽  
Constant Force ◽  
Parallel Mechanisms ◽  
End Effector ◽  
Neutral Equilibrium ◽  
The Difference ◽  
Elastic Elements

Gravity compensation of spatial parallel manipulators is a relatively recent topic of investigation. Perfect balancing has been accomplished, so far, only for parallel mechanisms in which the weight of the moving platform is sustained by legs comprising purely rotational joints. Indeed, balancing of parallel mechanisms with translational actuators, which are among the most common ones, has been traditionally thought possible only by resorting to additional legs containing no prismatic joints between the base and the end-effector. This paper presents the conceptual and mechanical designs of a balanced Gough/Stewart-type manipulator, in which the weight of the platform is entirely sustained by the legs comprising the extensible jacks. By the integrated action of both elastic elements and counterweights, each leg is statically balanced and it generates, at its tip, a constant force contributing to maintaining the end-effector in equilibrium in any admissible configuration. If no elastic elements are used, the resulting manipulator is balanced with respect to the shaking force too. The performance of a study prototype is simulated via a model in both static and dynamic conditions, in order to prove the feasibility of the proposed design. The effects of imperfect balancing, due to the difference between the payload inertial characteristics and the theoretical/nominal ones, are investigated. Under a theoretical point of view, formal and novel derivations are provided of the necessary and sufficient conditions allowing (i) a body arbitrarily rotating in space to rest in neutral equilibrium under the action of general constant-force generators, (ii) a body pivoting about a universal joint and acted upon by a number of zero-free-length springs to exhibit constant potential energy, and (iii) a leg of a Gough/Stewart-type manipulator to operate as a constant-force generator.

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