scholarly journals Direct Geometrico-static Problem of Underconstrained Cable-Driven Parallel Robots With $n$ Cables

2015 ◽  
Vol 31 (2) ◽  
pp. 468-478 ◽  
Author(s):  
Ghasem Abbasnejad ◽  
Marco Carricato
Keyword(s):  
Static Problem ◽  
Parallel Robots

Direct Geometrico-Static Problem of Underconstrained Cable-Driven Parallel Robots With Three Cables1

2013 ◽  
Vol 5 (3) ◽  
Author(s):  
Marco Carricato
Keyword(s):  
Complete Solution ◽  
Static Problem ◽  
Parallel Robots ◽  
Homotopy Continuation ◽  
Complex Field ◽  
Efficient Computation ◽  
End Effector ◽  
Tensile Forces ◽  
Univariate Polynomial ◽  
The Ideal

This paper studies the direct geometrico-static problem (DGP) of underconstrained cable-driven parallel robots (CDPRs) with three cables. The task consists in determining the end-effector pose and the cable tensile forces when the cable lengths are assigned. The problem is challenging, because kinematics and statics are coupled, and they must be tackled simultaneously. An effective elimination procedure is proposed and a least-degree univariate polynomial free of spurious factors is obtained in the ideal governing the problem. This is proven to admit 156 solutions in the complex field. Several approaches for the efficient computation of the complete solution set are presented, including an eigenproblem formulation and homotopy continuation.

Inverse Geometrico-Static Problem of Underconstrained Cable-Driven Parallel Robots With Three Cables1

2013 ◽  
Vol 5 (3) ◽  
Author(s):  
Marco Carricato
Keyword(s):  
Complete Solution ◽  
Static Problem ◽  
Parallel Robots ◽  
Solution Sets ◽  
Real Solutions

This paper studies underconstrained cable-driven parallel robots (CDPRs) with three cables. A major challenge in the study of these robots is the intrinsic coupling between kinematics and statics, which must be tackled simultaneously. Effective elimination procedures are presented which provide the complete solution sets of the inverse geometrico-static problems (IGPs) with assigned orientation or position. In the former case, the platform orientation is given, whereas the platform position and the cable lengths and tensions must be computed. In the latter case, the platform position is known, whereas the platform orientation and the cable lengths and tensions are to be calculated. The described problems are proven to admit at the most 1 and 24 real solutions, respectively.

LATERAL VIBRATIONS OF BEAMS ON AN ELASTIC BASE AT CHANGING THE SUPPORTING CONDITIONS

2020 ◽  
Vol 91 (5) ◽  
pp. 70-76
Author(s):  
E.V. LEONTIEV ◽  
◽  
Keyword(s):  
Dynamic Behavior ◽  
Elastic Foundation ◽  
Dynamic Problem ◽  
Static Problem ◽  
Elastic Base ◽  
Design Model ◽  
Lateral Vibrations ◽  
Internal Forces ◽  
Vibration Loads ◽  
The Right

The paper considers the system "beam - elastic foundation", in which a beam with free edges was at first on a solid elastic foundation, but when a defect suddenly forms in the foundation under the right side of the beam, part of foundation was removed from design model. As a result of calculations performed by the method of initial parameters, the displacements and internal forces for the static problem are determined. The dynamic problem of determining the forces and displacements was solved, taking into account the three vibration loads F (t) = F sinγt applied at arbitrary points d when the conditions for supporting the right side of the beam on an elastic foundation were changed, the values of the dynamics coefficients were determined. Conditions are formulated that must be taken into account when analyzing the dynamic behavior of a structure under the influence of vibration loads in the case of a change in the conditions of bearing on an elastic foundation.

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