scholarly journals Identification of Eigen-Frequencies and Mode-Shapes of Beams with Continuous Distribution of Mass and Elasticity and for Various Conditions at Supports

2020 ◽  
Author(s):  
Triantafyllos K. Makarios
Keyword(s):  
Degrees Of Freedom ◽  
Inverted Pendulum ◽  
Mass Matrix ◽  
Continuous Distribution ◽  
Local Network ◽  
Mode Shapes ◽  
Fundamental Frequencies ◽  
First Case ◽  
Three Degree Of Freedom ◽  
Three Degrees Of Freedom

In the present article, an equivalent three degrees of freedom (DoF) system of two different cases of inverted pendulums is presented for each separated case. The first case of inverted pendulum refers to an amphi-hinge pendulum that possesses distributed mass and stiffness along its height, while the second case of inverted pendulum refers to an inverted pendulum with distributed mass and stiffness along its height. These vertical pendulums have infinity number of degree of freedoms. Based on the free vibration of the above-mentioned pendulums according to partial differential equation, a mathematically equivalent three-degree of freedom system is given for each case, where its equivalent mass matrix is analytically formulated with reference on specific mass locations along the pendulum height. Using the three DoF model, the first three fundamental frequencies of the real pendulum can be identified with very good accuracy. Furthermore, taking account the 3 × 3 mass matrix, it is possible to estimate the possible pendulum damages using a known technique of identification mode-shapes via records of response accelerations. Moreover, the way of instrumentation with a local network by three accelerometers is given via the above-mentioned three degrees of freedom.

scholarly journals Identification of Mode-shapes and Eigen-frequencies of Bi-hinge Beam with Distributed Mass and Stiffness

2020 ◽  
Vol 9 (3) ◽  
pp. 119-126
Author(s):  
Triantafyllos K. Makarios
Keyword(s):  
Differential Equation ◽  
Mass Matrix ◽  
Degree Of Freedom ◽  
Local Network ◽  
Mode Shapes ◽  
Specific Mass ◽  
Concentrated Mass ◽  
Equivalent Mass ◽  
Eigen Frequencies ◽  
Three Degree Of Freedom

 In the present paper, an equivalent Three Degree of Freedom (DoF) system of a bi-hinge beam, which has infinity number of degree of freedoms because possesses distributed mass and stiffness along its length, is presented. Based on the vibration partial differential equation of the abovementioned bi-hinge beam, an equivalent, mathematically, three-degree of freedom system, where the equivalent mass matrix is analytically formulated with reference on specific mass locations. Using the Three DoF model, the first three fundamental mode-shapes of the real beam can be identified. Furthermore, taking account the 3x3 mass matrix, it is possible to estimate the possible beam damages using a known technique of identification mode-shapes via records of response accelerations. Moreover, the way of instrumentation with a local network by three accelerometers is shown. It is worth noting this technique can be applied on bridges consist of bays with two hinges at its end sections, supported on elastometallic bearings, where the sense of concentrated mass is fully absent from the beam.

Design of a Teaching Robot with Three Degrees of Freedom

2012 ◽  
Vol 619 ◽  
pp. 325-328
Author(s):  
You Jun Huang ◽  
Ze Lun Li ◽  
Zhi Cheng Huang
Keyword(s):  
Degrees Of Freedom ◽  
Low Cost ◽  
Degree Of Freedom ◽  
Good Repeatability ◽  
Main Components ◽  
Opening And Closing ◽  
Three Degree Of Freedom ◽  
Three Degrees Of Freedom ◽  
Application Prospects

A teaching robot with three degree of freedom is designed. The three degrees of freedom are: waist rotation, lifting and stretching of the arm and opening and closing of the gripper. The designs of the main components are: a mobile chassis, parallel rails, horizontal rails and manipulator. The teaching robot designed has the features of low cost, easy to regulation, good repeatability and it has good promotion and application prospects in the field of teaching.

Architecture Optmization of a 3-DOF Parallel Mechanism

1998 ◽  
Author(s):  
J. A. Carretero ◽  
R. P. Podhorodeski ◽  
M. Nahon
Keyword(s):  
Parallel Mechanism ◽  
Architectural Design ◽  
Degrees Of Freedom ◽  
Jacobian Matrix ◽  
Design Parameters ◽  
Objective Functions ◽  
Constraint Equations ◽  
Three Degree Of Freedom ◽  
Architecture Optimization ◽  
Three Degrees Of Freedom

Abstract This paper presents a study of the architecture optimization of a three-degree-of-freedom parallel mechanism intended for use as a telescope mirror focussing device. The construction of the mechanism is first described. Since the mechanism has only three degrees of freedom, constraint equations describing the inter-relationship between the six Cartesian coordinates are given. These constraints allow us to define the parasitic motions and, if incorporated into the kinematics model, a constrained Jacobian matrix can be obtained. This Jacobian matrix is then used to define a dexterity measure. The parasitic motions and dexterity are then used as objective functions for the optimizations routines and from which the optimal architectural design parameters are obtained.

scholarly journals Input Rationality Analysis of Three Degree of freedom Parallel Mechanism with Limbs of Embedding Structures

2019 ◽  
Vol 10 (2) ◽  
pp. 343-353
Author(s):  
Gaowei Yang ◽  
Jianjun Zhang ◽  
Weimin Li ◽  
Kaicheng Qi
Keyword(s):  
Parallel Mechanism ◽  
Group Selection ◽  
Degrees Of Freedom ◽  
Selection Rule ◽  
Direct Application ◽  
Input Selection ◽  
Selection Theory ◽  
Coupling Relationship ◽  
Three Degree Of Freedom ◽  
Three Degrees Of Freedom

Abstract. Three degrees of freedom (3-DoF) parallel mechanism (PM) with limbs of embedding structures is a kind of PM with a coupling relationship between limbs. In order to obtain a more desirable motion, the analysis of its actuated pairs shall be conducted. However, the fact that the existence of limbs coupling results in non-unique limb group, this mechanism has multiple limb groups. In this regard, the traditional input selection theory is not suitable for direct application in the input rationality analysis. Aiming to avoid this, a general extended input selection theory and limb group selection rule are proposed. The former tackles the traditional input selection theory which is not suitable for analyzing the input of PM with limbs of embedding structures since it does not take the influence of group into consideration, whereas the latter makes the calculation of the former easier. Based on the extended input selection theory and the limb group selection rule, the input and configuration of the 3-DoF PM with limbs of embedding structures are improved.

A Simple Spring-Loaded Inverted Pendulum (SLIP) Model of a Bio-Inspired Quadrupedal Robot Over Compliant Terrains

2018 ◽  
Author(s):  
Hasti Hayati ◽  
Paul Walker ◽  
Terry Brown ◽  
Paul Kennedy ◽  
David Eager
Keyword(s):  
Degrees Of Freedom ◽  
Inverted Pendulum ◽  
Viscoelastic Behavior ◽  
Slip Model ◽  
Runge Kutta Method ◽  
Synthetic Rubber ◽  
Spring Loaded Inverted Pendulum ◽  
Single Support Phase ◽  
The Impact ◽  
Three Degrees Of Freedom

To study the impact of compliant terrains on the biomechanics of rapid legged movements, a well-known spring loaded inverted pendulum (SLIP) model is deployed. The model is a three-degrees-of-freedom system (3 DOF), inspired by galloping greyhounds competing in a racing condition. A single support phase of hind-leg stance in a galloping gait is taken into consideration due to its primary function in powering the greyhounds locomotion and higher rate of musculoskeletal injuries. To obtain and solve the nonlinear second-order differential equation of motions, the Lagrangian method and MATLABb R2017b (ode45 solver), which is based on the Runge-Kutta method, has been used, respectively. To get the viscoelastic behavior of compliant terrains, a Clegg hammer test was developed and performed five times on each sample. The effective spring and damping coefficients of each sample were then determined from the hysteresis curves. The results showed that galloping on the synthetic rubber requires more muscle force compared with wet sand. However, according to the Clegg hammer test, wet sand had a higher impact force than synthetic rubber which can be a risk factor for bone fracture, particularly hock fracture, in greyhounds. The results reported in this paper are not only useful for identifying optimum terrain properties and injury thresholds of an athletic track, but also can be used to design control methods and shock impedances for legged robots performing on compliant terrains.

Utilization of Cable Guide Channels for Compact Articulation Within a Dexterous Three Degrees-of-Freedom Surgical Wrist Design

2018 ◽  
Vol 13 (1) ◽  
Author(s):  
Dale J. Podolsky ◽  
Eric Diller ◽  
David M. Fisher ◽  
Karen W. Wong Riff ◽  
Thomas Looi ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Small Body ◽  
Body Cavity ◽  
Cable Tension ◽  
Actuation Mechanism ◽  
3D Printed ◽  
Path Lengths ◽  
Three Degree Of Freedom ◽  
Robotic Applications ◽  
Three Degrees Of Freedom

Pin-jointed wrist mechanisms provide compact articulation for surgical robotic applications, but are difficult to miniaturize at scales suitable for small body cavity surgery. Solid surface cable guide channels, which eliminate the need for pulleys and reduce overall length to facilitate miniaturization, were developed within a three-degree-of-freedom cable-driven pin-jointed wrist mechanism. A prototype was 3D printed in steel at 5 mm diameter. Friction generated by the guide channels was experimentally tested to determine increases in cable tension during constant cable velocity conditions. Cable tension increased exponentially from 0 to 37% when the wrist pitched from 0 deg to 90 deg. The shape of the guide channel groove and angle, where the cable exits the channel impacts the magnitude of cable tension. A spring tensioning and cam actuation mechanism were developed to account for changing cable circuit path lengths during wrist pitch. This work shows that pulley-free cable wrist mechanisms can facilitate miniaturization below current feasible sizes while retaining compact articulation at the expense of increases in friction under constant cable velocity conditions.

Topological and Geometrical Synthesis of Three-Degree-of-Freedom Fully Parallel Manipulators by Instantaneous Kinematics

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
Xiaoyu Wang ◽  
Luc Baron ◽  
Guy Cloutier
Keyword(s):  
Degrees Of Freedom ◽  
Parallel Manipulators ◽  
Synthesis Process ◽  
End Effector ◽  
Numerical Examples ◽  
Passive Joint ◽  
New Synthesis ◽  
Synthesis Procedure ◽  
Three Degree Of Freedom ◽  
Three Degrees Of Freedom

This paper presents a new synthesis procedure of fully parallel manipulators (PMs) of three degrees of freedom (DOFs) that could be implemented in a computer-aided synthesis process. Possible designs of PMs are represented by a set of unit joint twists at an initial configuration, called here topological and geometric parameters (TGPs). This makes it possible to represent PMs of all topologies and geometries in an easy and consistent way. The kinematic bond between the end effector (EE) and the base is then formulated as a set of equations involving TGPs, actuated-joint variables, and non-actuated-joint variables (passive joints). To achieve the required type of EE motion, possible topologies are first derived from tangent space analysis, and then the feasible topologies are retained by further displacement analysis. The geometries are determined such that the set of equations should be isoconstrained when passive-joint variables are taken as unknowns. The synthesis procedure of 3DOF PMs is illustrated with three numerical examples: one producing a new architecture of one translation and two rotations, while the other two producing existing architectures of translational PMs.

scholarly journals Discrete Motion Prediction Based on EMG Signals

2019 ◽  
Vol 37 (3) ◽  
pp. 509-514
Author(s):  
Lei Zhang ◽  
Wendong Wang ◽  
Yikai Shi ◽  
Jiahao Liu ◽  
Yang Chu ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Control Method ◽  
Recognition Accuracy ◽  
Robot Arm ◽  
Accuracy Rate ◽  
Exoskeleton Robot ◽  
Designed Experiment ◽  
Three Degree Of Freedom ◽  
Discrete Motion ◽  
Three Degrees Of Freedom

Most of the current rehabilitation equipment is bulky and slow to respond. Therefore, we designed a portable three-degree-of-freedom exoskeleton and discrete-mode control system for this situation. The three degrees of freedom of the exoskeleton robot arm was the wrist swing, the forearm lateral movement, and the elbow rotation. We collected the EMG signals of the biceps and triceps, then filtered the acquired EMG signals and extracted features in order to obtain effective information that reflected the activity intentions. Based on this, a discrete motion control method using the EMG signals to achieve elbow rotation was designed. Experiment suggests that the average pattern recognition accuracy rate can reach more than 90%.

Kinematic Analysis of a Three-DOF Parallel Mechanism for Telescope Applications

1997 ◽  
Author(s):  
J. A. Carretero ◽  
M. Nahon ◽  
B. Buckham ◽  
C. M. Gosselin
Keyword(s):  
Kinematic Analysis ◽  
Inverse Kinematics ◽  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Jacobian Matrix ◽  
Constraint Equations ◽  
Forward And Inverse Kinematics ◽  
Position And Orientation ◽  
Three Degree Of Freedom ◽  
Three Degrees Of Freedom

Abstract This paper presents a kinematic analysis of a three-degree-of-freedom parallel mechanism intended for use as a telescope mirror focussing device. The construction of the mechanism is first described and its forward and inverse kinematics solutions are derived. Because the mechanism has only three degrees of freedom, constraint equations must be generated to describe the inter-relationship between the six Cartesian coordinates which describe the position and orientation of the moving platform. Once these constraints are incorporated into the kinematics model, a constrained Jacobian matrix is obtained. The stiffness and dexterity properties of the mechanism are then determined based on this Jacobian matrix. The mechanism is shown to exhibit desirable properties in the region of its workspace of interest in the telescope focussing application.

Generalized Component Mode Synthesis for the Spatial Motion of Flexible Bodies With Large Rotations About One Axis1

2016 ◽  
Vol 11 (4) ◽  
Author(s):  
Pascal Ziegler ◽  
Alexander Humer ◽  
Astrid Pechstein ◽  
Johannes Gerstmayr
Keyword(s):  
Multibody Systems ◽  
Velocity Vector ◽  
Degrees Of Freedom ◽  
Mass Matrix ◽  
Component Mode Synthesis ◽  
Mode Shapes ◽  
State Dependency ◽  
Large Rotations ◽  
Flexible Deformation ◽  
Quadratic Velocity Vector

In industrial practice, the floating frame of reference formulation (FFRF)—often combined with the component mode synthesis (CMS) in order to reduce the number of flexible degrees-of-freedom—is the common approach to describe arbitrarily shaped bodies in flexible multibody systems. Owed to the relative formulation of the flexible deformation with respect to the reference frame, the equations of motion show state-dependent nonconstant inertia terms. Such relative description, however, comes along with considerable numerical costs, since both the mass matrix and gyroscopic forces, i.e., the quadratic velocity vector, need to be evaluated in every integration step. The state dependency of the inertia terms can be avoided by employing an alternative formulation based on the mode shapes as in the classical CMS approach. In this approach, which is referred to as generalized component mode synthesis (GCMS), the total (absolute) displacements are approximated directly. Consequently, the mass matrix is constant, no quadratic velocity vector appears, and the stiffness matrix is a corotated but otherwise constant matrix. In order to represent the same flexible deformation as in the classical FFRF-based CMS, however, a comparatively large number of degrees-of-freedom is required. The approach described in the present paper makes use of the fact that a majority of components in technical systems are constrained to motions showing large rotations only about a single spatially fixed axis. For this reason, the GCMS is adapted for multibody systems that are subjected to small flexible deformations and undergo a rigid body motion showing large translations, large rotations about one axis, but small rotations otherwise. Thereby, the number of shape functions representing the flexible deformation is reduced, which further increases numerical efficiency compared to the original GCMS formulation for arbitrary rotations.

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