Synthesis of Seven-Link Mechanisms

1973 ◽  
Vol 95 (2) ◽  
pp. 533-540 ◽  
Author(s):  
D. Kohli ◽  
A. H. Soni
Keyword(s):  
Closed Form ◽  
Nonlinear Equations ◽  
Degrees Of Freedom ◽  
The Other ◽  
Linear Superposition ◽  
Two Degrees Of Freedom ◽  
Closed Form Solutions ◽  
Highly Nonlinear ◽  
Principle Of Linear Superposition

The mechanisms derived from the seven-link chains with five links in their two loops and having two degrees of freedom are examined for six synthesis problems. Using displacement matrices, closed form synthesis equations are derived. It is shown that three synthesis problems may be solved using the principle of linear superposition, and closed form solutions may be obtained. The other three synthesis problems involve highly nonlinear equations and must be solved numerically.

scholarly journals Reliability of Sampling Inspection Schemes Applied to Replacement Steam Generators

2006 ◽  
Vol 129 (1) ◽  
pp. 109-117 ◽  
Author(s):  
Guy Roussel ◽  
Leon Cizelj
Keyword(s):  
Closed Form ◽  
Steam Generator ◽  
The State ◽  
The Other ◽  
Prior Density ◽  
Steam Generators ◽  
Numerical Examples ◽  
Closed Form Solutions ◽  
Sampling Inspection ◽  
Steam Generator Tubing

The basis for determining the size of the random sample of tubes to be inspected in replacement steam generators is revisited in this paper. A procedure to estimate the maximum number of defective tubes left in the steam generator after no defective tubes have been detected in the randomly selected inspection sample is proposed. A Bayesian estimation is used to obtain closed-form solutions for uniform, triangular, and binomial prior densities describing the number of failed tubes in steam generators. It is shown that the particular way of selecting the random inspection sample (e.g., one sample from both SG, one sample from each SG, etc.) does not affect the results of the inspection and also the information obtained about the state of the uninspected tubing, as long as the inspected steam generators belong to the same population. Numerical examples further demonstrate two possible states of the knowledge existing before the inspection of the tubing. First, virtually no knowledge about the state of the steam generator tubing before the inspection is modeled using uniform and triangular prior densities. It is shown that the knowledge about the uninspected part of the tubing strongly depends on the size of the sample inspected. Further, even small inspection samples may significantly improve our knowledge about the uninspected part. On the other hand, rather strong belief on the state of the tubing prior to the inspection is modeled using binomial prior density. In this case, the knowledge about the uninspected part of the tubing is virtually independent on the size of the sample. Furthermore, it is shown qualitatively and quantitatively that such inspection brings no additional knowledge on the uninspected part of the tubing.

The Conceptual Design of Differential Mechanisms

2013 ◽  
Vol 284-287 ◽  
pp. 973-978
Author(s):  
Chia Chun Chu
Keyword(s):  
Conceptual Design ◽  
Design Process ◽  
Degrees Of Freedom ◽  
Geometric Constraints ◽  
The Other ◽  
Design Approach ◽  
Process Step ◽  
Two Degrees Of Freedom ◽  
Number Synthesis

The purpose of this paper is to present a design approach based on the geometric constraints of joints for synthesizing differential mechanisms with two degrees-of-freedom, including some mechanisms with the same functions but distinct structures. The concept of virtual axes is presented. And, there are five steps in the design process. Step 1 is to decide fundamental entities by the properties of existing mechanisms and the technique of number synthesis, and 10 suitable fundamental entities of differential mechanisms are available. Step 2 is to compose geometric constraints, and 14 items are obtained. Step 3 is to compose links, and 15 items are derived. Step 4 is to assign fixed constraints for inputs or outputs, and 15 results are found. The final step is to particularize the obtained events by the properties of existing mechanisms and the structures of fundamental entities. As a result, 8 feasible results for differential mechanisms with two degrees-of-freedom and two basic loops are obtained in which 2 are existing designs and the other 6 are novel.

Geometry and Position Analysis of a Novel Class of Hybrid Manipulators

1994 ◽  
Author(s):  
Change-de Zhang ◽  
Shin-Min Song
Keyword(s):  
Closed Form ◽  
Degrees Of Freedom ◽  
Parallel Manipulators ◽  
Parallel Mechanisms ◽  
Serial Manipulators ◽  
Closed Form Solutions ◽  
Position Analysis ◽  
Hybrid Manipulator ◽  
Load Carrying ◽  
Inverse Position Analysis

Abstract This paper presents a novel class of hybrid manipulators composed of two serially connected parallel mechanisms, each of which has three degrees of freedom. The lower and upper platforms respectively control the position and orientation of the end-effector. The advantages of this type of hybrid manipulator are larger workspace (as compared with parallel manipulators) and better rigidity and higher load-carrying capability (as compared with serial manipulators). The closed-form solutions of the forward and inverse position analyses are discussed. For forward position analysis, it is shown that the resultant equation for the positional mechanism is an 8-th order, a 6-th order, a 4-th order, or a 2-nd order polynomial, depending on the geometry and joint types of the passive subchain, while for the orientational mechanism, it is an 8-th order, or a 2-nd polynomial depending on the geometry. For inverse position analysis, it is demonstrated that the positional and orientational mechanisms both possess analytical closed-form solutions.

Adaptive neuro-fuzzy inference system–based path planning of 5-degrees-of-freedom spatial manipulator for medical applications

2018 ◽  
Vol 232 (7) ◽  
pp. 726-732 ◽  
Author(s):  
Jyotindra Narayan ◽  
Ekta Singla ◽  
Sanjeev Soni ◽  
Ashish Singla
Keyword(s):  
Path Planning ◽  
Closed Form ◽  
Fuzzy Inference System ◽  
Degrees Of Freedom ◽  
Fuzzy Inference ◽  
Inverse Kinematic ◽  
Inference System ◽  
Closed Form Solutions ◽  
Neuro Fuzzy ◽  
Patient Side

Over the last few decades, medical-assisted robots have been considered by many researchers, within the research domain of robotics. In this article, a 5-degrees-of-freedom spatial medical manipulator is analyzed for path planning, based on inverse kinematic solutions. Analytical methods have generally employed for finding the inverse kinematic solutions in earlier studies. However, this method is only appreciable in case of closed-form solutions. The unusual joint configurations of considered manipulator result in more complexity to attain the closed-form solutions, analytically. To overcome with shortcomings of analytical method, a non-traditional approach named adaptive neuro-fuzzy inference system is proposed under the class of artificial intelligent techniques. This article presents this neuro-fuzzy approach for desired path generation by 5-degrees-of-freedom manipulator. The estimation of percentage error between actual path and adaptive neuro-fuzzy inference system–generated path is done with respect to x, y, and z directions, respectively. Furthermore, the error between actual and predicted values regarding joint parameters is calculated for a certain arm matrix. The prototype of 5-degrees-of-freedom medical-assisted manipulator is developed at CSIR-CSIO Laboratory Chandigarh, which is also termed as patient-side manipulator to be utilized in robot-assisted surgery. Through the simulation runs, in this work, it is found that the results from adaptive neuro-fuzzy inference system approach are quite satisfactory and acceptable.

scholarly journals Existence Conditions and General Solutions of Closed-form Inverse Kinematics for Revolute Serial Robots

2019 ◽  
Vol 9 (20) ◽  
pp. 4365 ◽  
Author(s):  
Wang Shanda ◽  
Luo Xiao ◽  
Luo Qingsheng ◽  
Han Baoling
Keyword(s):  
Closed Form ◽  
Inverse Kinematics ◽  
Degrees Of Freedom ◽  
Closed Form Solution ◽  
Form Solution ◽  
Algebraic Equations ◽  
Closed Form Solutions ◽  
Serial Robots ◽  
Existence Conditions ◽  
Low Degrees

This study proposes a method for judging the existence of closed-form inverse kinematics solutions based on the Denavit–Hartenberg (DH) model. In this method, serial robots with closed-form solutions are described using three types of sub-problems from the viewpoint of solving algebraic equations. If a serial robot can be described using these three types of sub-problems, i.e., if the inverse kinematics problems can be solved by several basic problems, then there is a closed-form solution. Based on the above method, we design a set of universal closed-form inverse kinematics solving algorithms. Since there is a definite formula solution for the three types of sub-problems, the joint angles can be rapidly determined. In addition, because the DH parameters can directly reflect the linkage of the robot, the judgment of the sub-problems is also quick and accurate. More importantly, the algorithm can be applied to serial robots with low degrees of freedom. This enables the algorithm to not only quickly and accurately solve inverse kinematics problems but also to exhibit high universality. This proposed theory improves the existence conditions for closed-form reverse solutions and further promotes the development of motion control techniques for serial robots.

Kinematics of Continuum Robots With Constant Curvature Bending and Extension Capabilities

2018 ◽  
Vol 11 (1) ◽  
Author(s):  
Arnau Garriga-Casanovas ◽  
Ferdinando Rodriguez y Baena
Keyword(s):  
Closed Form ◽  
Inverse Kinematics ◽  
Degrees Of Freedom ◽  
Rapid Development ◽  
Closed Form Expression ◽  
Great Promise ◽  
Continuum Robots ◽  
Cluttered Environments ◽  
Closed Form Solutions ◽  
Significant Attention

Continuum robots are becoming increasingly popular due to the capabilities they offer, especially when operating in cluttered environments, where their dexterity, maneuverability, and compliance represent a significant advantage. The subset of continuum robots that also belong to the soft robots category has seen rapid development in recent years, showing great promise. However, despite the significant attention received by these devices, various aspects of their kinematics remain unresolved, limiting their adoption and obscuring their potential. In this paper, the kinematics of continuum robots with the ability to bend and extend are studied, and analytical, closed-form solutions to both the direct and inverse kinematics are presented. The results obtained expose the redundancies of these devices, which are subsequently explored. The solution to the inverse kinematics derived here is shown to provide an analytical, closed-form expression describing the curve associated with these redundancies, which is also presented and analyzed. A condition on the reachable end-effector poses for robots with six actuation degrees-of-freedom (DOFs) is then distilled. The kinematics of robot layouts with over six actuation DOFs are subsequently considered. Finally, simulated results of the inverse kinematics are provided, verifying the study.

Two-Degree-of-Freedom Decoupled Nonredundant Cable-Loop-Driven Parallel Mechanism

2013 ◽  
Vol 6 (1) ◽  
Author(s):  
Hanwei Liu ◽  
Clément Gosselin ◽  
Thierry Laliberté
Keyword(s):  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Degree Of Freedom ◽  
The Other ◽  
End Effector ◽  
Two Degrees Of Freedom ◽  
Actuation Redundancy ◽  
Rigid Link ◽  
Force Closure ◽  
Two Degree Of Freedom

A novel two-degree-of-freedom (DOF) cable-loop slider-driven parallel mechanism is introduced in this paper. The novelty of the mechanism lies in the fact that no passive rigid-link mechanism or springs are needed to support the end-effector (only cables are connected to the end-effector) while at the same time there is no actuation redundancy in the mechanism. Sliders located on the edges of the workspace are used and actuation redundancy is eliminated while providing force closure everywhere in the workspace. It is shown that the two degrees of freedom of the mechanism are decoupled and only two actuators are needed to control the motion. There are two cable loops for each direction of motion: one acts as the actuating loop while the other is the constraint loop. Due to the simple geometric design, the kinematic and static equations of the mechanism are very compact. The stiffness of the mechanism is also analyzed in the paper. It can be observed that the mechanism's stiffness is much higher than the stiffness of the cables. The proposed mechanism's workspace is essentially equal to its footprint and there are no singularities.

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