Modeling the Compliance of a Variable Stiffness C-Shaped Leg Using Castigliano’s Theorem

2010 ◽  
Author(s):  
Yasemin O¨. Aydın ◽  
Kevin C. Galloway ◽  
Yigit Yazicioglu ◽  
Daniel E. Koditschek
Keyword(s):  
Rigid Body ◽  
Closed Form ◽  
Variable Stiffness ◽  
Dynamic Equations ◽  
Hexapod Robot ◽  
Static Loads ◽  
Compliant Robot ◽  
Circular Beam ◽  
Robot Leg ◽  
Castigliano’S Theorem

This paper discusses the application of Castigliano’s Theorem to a half circular beam intended for use as a shaped, tunable, passively compliant robot leg. We present closed-form equations characterizing the deflection behavior of the beam (whose compliance properties vary along the leg) under appropriate loads. We compare the accuracy of this analytical representation to that of a Pseudo Rigid Body (PRB) approximation in predicting the data obtained by measuring the deflection of a physical half-circular beam under the application of known static loads. We briefly discuss the further application of the new model for solving the dynamic equations of a hexapod robot with a C-shaped leg.

scholarly journals Closed-form time derivatives of the equations of motion of rigid body systems

2021 ◽  
Author(s):  
Andreas Müller ◽  
Shivesh Kumar
Keyword(s):  
Rigid Body ◽  
Closed Form ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
Alternative Formulation ◽  
Dynamics Of Rigid Body ◽  
Control Forces ◽  
And Control ◽  
Derivatives Of ◽  
Insight Into

AbstractDerivatives of equations of motion (EOM) describing the dynamics of rigid body systems are becoming increasingly relevant for the robotics community and find many applications in design and control of robotic systems. Controlling robots, and multibody systems comprising elastic components in particular, not only requires smooth trajectories but also the time derivatives of the control forces/torques, hence of the EOM. This paper presents the time derivatives of the EOM in closed form up to second-order as an alternative formulation to the existing recursive algorithms for this purpose, which provides a direct insight into the structure of the derivatives. The Lie group formulation for rigid body systems is used giving rise to very compact and easily parameterized equations.

scholarly journals Application of the dynamic Lorentz model to modeling the motion of a rigid body

2021 ◽  
pp. 32-36
Author(s):  
Nikolay Makeyev ◽  
Keyword(s):  
Dynamical System ◽  
Qualitative Research ◽  
Rigid Body ◽  
Body Motion ◽  
Dynamic Equations ◽  
Lorentz Model ◽  
Dissipative Forces ◽  
System Parameters ◽  
Phase Trajectories ◽  
Inertia Forces

A qualitative research of the field of phase trajectories of the system of dynamic equations of an absolutely rigid body was carried out, moving around the selected pole under the influence of gyroscopic, dissipative forces and Coriolis inertia forces. The equations of body motion are reduced to a dynamical system generating a Lorentz attractor. Under parametric constraints imposed on the equations of a dynamical system, the structure of its phase trajectories is described depending on the values of the system parameters.

scholarly journals On a CPG-Based Hexapod Robot: AmphiHex-II With Variable Stiffness Legs

2018 ◽  
Vol 23 (2) ◽  
pp. 542-551 ◽  
Author(s):  
Bin Zhong ◽  
Shiwu Zhang ◽  
Min Xu ◽  
Youcheng Zhou ◽  
Tao Fang ◽  
...  
Keyword(s):  
Variable Stiffness ◽  
Hexapod Robot
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