Equivalent Kinematic Chains of Three Degree-of-Freedom Tripod Mechanisms With Planar-Spherical Bonds

2005 ◽  
Vol 127 (1) ◽  
pp. 95-102 ◽  
Author(s):  
Patrick Huynh ◽  
Jacques M. Herve´
Keyword(s):  
Closed Loop ◽  
Degree Of Freedom ◽  
Robotic Device ◽  
Kinematics Analysis ◽  
Closed Loop System ◽  
Short Introduction ◽  
Kinematic Chains ◽  
Displacement Group ◽  
Three Degree Of Freedom ◽  
Moving Spheres

The paper aims to analyze the equivalent kinematic chains of a family of three-degree-of-freedom (3-DOF) tripod mechanisms with planar-spherical bonds in order to determine the platform motions generated by the mechanisms, and then to develop a prototype of a 3-DOF 3-RPS type parallel mechanism, which can be used as a wrist robotic device. After a short introduction to mechanical generators of Lie subgroups of displacement, the mobility formula of a general 3-DOF tripod mechanism based on the modified Gru¨ebler’s criterion is given. Using displacement group theory theorems, the analyzed closed-loop system becomes finally equivalent to three contacts between a rigid assembly of three moving spheres onto three fixed planes. As an application of the above method, a prototype mechanism is designed and fabricated based on the kinematics analysis, the force capability and the simplicity.

Stability Analysis of a Bilateral Teleoperating System

1993 ◽  
Vol 115 (3) ◽  
pp. 419-426 ◽  
Author(s):  
Y. Strassberg ◽  
A. A. Goldenberg ◽  
J. K. Mills
Keyword(s):  
Feedback Linearization ◽  
Closed Loop ◽  
Tracking Error ◽  
Degree Of Freedom ◽  
Closed Loop System ◽  
Control Scheme ◽  
Feedback Linearization Control ◽  
Small Gain ◽  
The Stability ◽  
Three Degree Of Freedom

In this paper the stability of a control scheme for bilateral master-slave teleoperation is investigated. Given the nominal models of the master and slave dynamics, and using an approximate feedback linearization control, based on the earlier work of Spong and Vidyasagar, 1987, a robust closed-loop system (position and force) can be obtained with a multiloop version of the small gain theorem. It is shown that stable bilateral teleoperating systems can be achieved under the assumption that the deviation of the models from the actual systems satisfies certain norm inequalities. We also show that, using the proposed scheme, the tracking error (position/velocity and force/torque) is bounded and it can be made arbitrarily small. The control scheme is illustrated using the simulation of a three-degree-of-freedom master-slave teleoperator (three-degree-of-freedom master and three-degree-of-freedom slave).

Parametric Design of a Spherical Eight-Bar Linkage Based on a Spherical Parallel Manipulator

2008 ◽  
Vol 1 (1) ◽  
Author(s):  
Gim Song Soh ◽  
J. Michael McCarthy
Keyword(s):  
Inverse Kinematics ◽  
Parallel Manipulator ◽  
Parametric Design ◽  
Degree Of Freedom ◽  
Kinematics Analysis ◽  
End Effector ◽  
Arbitrary Base ◽  
Three Degree Of Freedom ◽  
Spherical Parallel Manipulator

This paper presents a procedure that determines the dimensions of two constraining links to be added to a three degree-of-freedom spherical parallel manipulator so that it becomes a one degree-of-freedom spherical (8, 10) eight-bar linkage that guides its end-effector through five task poses. The dimensions of the spherical parallel manipulator are unconstrained, which provides the freedom to specify arbitrary base attachment points as well as the opportunity to shape the overall movement of the linkage. Inverse kinematics analysis of the spherical parallel manipulator provides a set of relative poses between all of the links, which are used to formulate the synthesis equations for spherical RR chains connecting any two of these links. The analysis of the resulting spherical eight-bar linkage verifies the movement of the system.

A distinct matrix representation of the planar kinematic chains and isomorphism recognition

2019 ◽  
Vol 13 (4) ◽  
pp. 5717-5734
Author(s):  
M. S. Alam ◽  
M. Suhaib
Keyword(s):  
Mechanism Design ◽  
Design Problem ◽  
Matrix Representation ◽  
Degree Of Freedom ◽  
New Method ◽  
Structural Synthesis ◽  
Primary Condition ◽  
Secondary Conditions ◽  
Kinematic Chains ◽  
Three Degree Of Freedom

Structural synthesis of kinematic chains has been an indispensable area of the mechanism-design problem. The duplication may occur while developing kinematic chains. Therefore, an isomorphic test is required to eliminate duplication. For this purpose, the numbers of methods are proposed during recent years. However, most of the methods are complex and difficult to understand, and fulfil the only primary condition, but not the secondary conditions for isomorphism detection. In the present work, a new method is introduced to detect isomorphism in planar kinematic chains (KCs) fulfilling both primary and secondary conditions. First, KC’s are topologically transformed into skeleton diagrams, and then skeleton matrices [S] and identification strings [IS] are formulated consequently. In order to detect isomorphism, the IS is considered as an invariant string of a KC which in turn, enables the detection of isomorphism between the KCs. The proposed method accurately recognizes isomorphism up to 12 links KCs with no counter examples found in the literature. Three examples with one degree of freedom having 10 links 12 joints, 10 links 13 joints and 12 links three degree of freedom systems are introduced to reveal the reliability and strength of the proposed method.

A New Algorithm for the Determination of the Workspace of Complex Planar Kinematic Chains

1995 ◽  
Author(s):  
Pascal Lê-Huu ◽  
Clément M. Gosselin
Keyword(s):  
Numerical Solution ◽  
Inverse Kinematics ◽  
Degree Of Freedom ◽  
Topological Graph ◽  
Kinematic Chains ◽  
Cartesian Space ◽  
Hybrid Manipulator ◽  
Three Degree Of Freedom ◽  
Two Degree Of Freedom

Abstract A new algorithm for the determination of the workspace of complex planar kinematic chains is presented in this paper. This algorithm is completely general since it can deal with any kind of topological graph and any set of parameters defined in a convention of notation. It uses the numerical solution of the inverse kinematics and is based on a wavefront expansion in the Cartesian space. Three examples are presented here, and lead to a dexterity mapping for two two-degree-of-freedom multi-loop manipulators and a three-degree-of-freedom hybrid manipulator.

scholarly journals Saturating Stiffness Control of Robot Manipulators with Bounded Inputs

2017 ◽  
Vol 27 (1) ◽  
pp. 79-90 ◽  
Author(s):  
María del Carmen Rodríguez-Liñán ◽  
Marco Mendoza ◽  
Isela Bonilla ◽  
César A. Chávez-Olivares
Keyword(s):  
Closed Loop ◽  
Robot Manipulator ◽  
Robot Manipulators ◽  
Contact Forces ◽  
Control Law ◽  
Closed Loop System ◽  
Control Scheme ◽  
Lyapunov Stability Analysis ◽  
Stiffness Control ◽  
Three Degree Of Freedom

AbstractA saturating stiffness control scheme for robot manipulators with bounded torque inputs is proposed. The control law is assumed to be a PD-type controller, and the corresponding Lyapunov stability analysis of the closed-loop equilibrium point is presented. The interaction between the robot manipulator and the environment is modeled as spring-like contact forces.The proper behavior of the closed-loop system is validated using a three degree-of-freedom robotic arm.

Two Degree-of-Freedom Hysteresis Compensation for a Dynamic Mirror With Antagonistic Piezoelectric Stack Actuation

2013 ◽  
Author(s):  
James A. Mynderse ◽  
George T. C. Chiu
Keyword(s):  
Input Signal ◽  
Control Strategy ◽  
Closed Loop ◽  
Loop System ◽  
Degree Of Freedom ◽  
Closed Loop System ◽  
Loop Control ◽  
Hysteresis Compensation ◽  
Hysteresis Control ◽  
Two Degree Of Freedom

A methodology for designing a low-computation, high-bandwidth strategy for closed-loop control of a hysteretic system without a priori knowledge of the desired trajectory is presented. The resulting two degree-of-freedom hysteresis control strategy is applied to a dynamic mirror with antagonistic piezoelectric stack actuation. Hysteresis compensator is performed by a finite state machine switching polynomials for hysteresis inversion based on the input signal slope. Residual error after hysteresis compensation is corrected by an LQR feedback controller. Experimental results demonstrate effectiveness of the hysteresis compensator and closed-loop system under the proposed hysteresis control strategy. For the triangular input signal tested, the closed-loop system achieves a 91.5% reduction in hysteresis uncertainty with 60 kHz sample rate.

Forward Position Analysis of Two 3-R Robots Manipulating a Planar Linkage Payload

1995 ◽  
Vol 117 (2A) ◽  
pp. 292-297 ◽  
Author(s):  
G. R. Pennock ◽  
K. G. Mattson
Keyword(s):  
Closed Loop ◽  
Degree Of Freedom ◽  
Sixth Order ◽  
Position Analysis ◽  
Revolute Joints ◽  
Order Polynomial ◽  
Cooperating Robots ◽  
Position Problem ◽  
Three Degree Of Freedom ◽  
Insight Into

This paper presents the forward position analysis of two planar three degree-of-freedom robots, with all revolute joints, manipulating a single degree-of-freedom closed-loop linkage payload. Kinematic constraint relations are developed which provide geometric insight into the cooperating robot-payload system and are important in the control of the two robots. For illustrative purposes, the payload that is considered here is a planar four-bar linkage. The paper shows that the orientation of a specified link in the payload can be described by a sixth-order polynomial. This polynomial is an important contribution, not only to the kinematics of the cooperating robots, but to the multiple-input closed-loop nine-bar linkage formed by the two robots and the payload. The polynomial contains important information regarding the assembly configurations and the stationary configurations of the system. The paper shows that zero, two, four, or six assembly configurations are possible and that each configuration corresponds to a different circuit of the system. Graphical methods are utilized to provide geometric insight into the assembly and stationary configurations and to check the results obtained from the sixth-order polynomial. A numerical example is included which demonstrates the importance of the polynomial in solving the forward position problem, and in determining the number of assembly configurations.

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