On the Derivation of Grashof-Type Movability Conditions With Transmission Angle Limitations for Spatial Mechanisms

1989 ◽  
Vol 111 (4) ◽  
pp. 519-523 ◽  
Author(s):  
J. Rastegar
Keyword(s):  
Approximation Techniques ◽  
Link Type ◽  
Revolute Joints ◽  
Spatial Mechanisms ◽  
Transmission Angle ◽  
Full Rotation ◽  
Drag Link

Derivation of Grashof-type movability conditions for spatial mechanisms that may include transmission angle limitations is discussed. It is shown that in general, different conditions must be derived for each configuration (branch) of a mechanism. In the absence of transmission angle limitations, the conditions become identical for pairs of configurations. As an example, Grashof-type conditions that ensure crank rotatability, existence of drag link type of mechanisms, the presence of single or multiple changeover points, and the possibility of full rotation at intermediate revolute joints are derived for a spatial RRRSR mechanism. The problems involved in such derivations, the use of approximation techniques, and a number of related subjects are discussed.

On the Derivation of Grashof-Type Moveability Conditions With Transmission Angle Control for Spatial Mechanisms

1987 ◽  
Author(s):  
J. Rastegar
Keyword(s):  
Approximation Techniques ◽  
Link Type ◽  
Revolute Joints ◽  
Spatial Mechanisms ◽  
Transmission Angle ◽  
Full Rotation ◽  
Drag Link

Abstract Derivation of Grashof-type conditions for spatial mechanisms that may include transmission angle limitations are discussed. It is shown that in general, different conditions need to be derived for each one of the existing configurations of the mechanism. In the absence of any transmission angle control, the conditions would be identical for pairs of configurations. As an example, for RRRSR mechanisms, Grashof-type conditions that ensure crank rotatability, the existence of a drag link type of mechanism, single or multiple changeover points, the possibility of full rotation at intermediate revolute joints, etc., are determined. A general discussion of the problems involved in such derivations, the use of approximation techniques to overcome some of the problems, and several other related subjects are presented.

Approximated Grashof-Type Movability Conditions for RSSR Mechanisms With Force Transmission Limitations

1992 ◽  
Vol 114 (1) ◽  
pp. 74-81 ◽  
Author(s):  
J. Rastegar ◽  
Q. Tu
Keyword(s):  
Closed Form ◽  
Closed Loop ◽  
Open Loop ◽  
Approximation Technique ◽  
Force Transmission ◽  
Output Link ◽  
Link Type ◽  
Spatial Mechanisms ◽  
Loop Chain ◽  
Drag Link

Closed-form Grashof-type movability conditions are derived for closed-loop RSSR mechanisms using a geometrical approximation technique. The conditions that ensure the presence of crank-rocker and drag-link type mechanisms are derived with and without force transmission limitations. The force transmission limitations may be specified as a function of the output link angle. The accuracy of the approximated conditions is analyzed. As an example, the conditions are used to synthesize a function generating mechanism with fully rotatable crank and with various force transmission requirements. The developed technique is general, and can be applied to other similar spatial mechanisms. The application of this approach to geometrical synthesis of open-loop chain manipulators is discussed.

On the Galloway-Type of Spatial Mechanisms

1990 ◽  
Vol 112 (4) ◽  
pp. 466-471
Author(s):  
J. Rastegar
Keyword(s):  
Geometric Parameters ◽  
Equal Length ◽  
Output Link ◽  
Spatial Mechanism ◽  
Numerical Example ◽  
Link Type ◽  
Spatial Mechanisms ◽  
Drag Link

The Galloway mechanism is a plane four-bar, drag-link-type linkage with one pair of equal-length shorter links, and one pair of equal-length longer links, forming a rhomboid geometry. The short links constitute the frame and the input links. In a Galloway mechanism, two full rotations of the input link result in a single rotation of the output link. In this paper, the Galloway mechanism is analyzed and the rules governing its motion are found. The conditions necessary for the existence of a Galloway-type spatial mechanism are then determined. As an example, the necessary relationships between the geometric parameters of a spatial RRRSR mechanism are derived. A numerical example is included.

Design of Centric Drag-Link Mechanisms for Delay Generation With Focus on Space Occupation

2008 ◽  
Vol 131 (1) ◽  
Author(s):  
Abdullah F. Al-Dwairi
Keyword(s):  
Length Ratio ◽  
Link Length ◽  
Link Mechanism ◽  
Maximum Delay ◽  
Transmission Angle ◽  
Quality Of Motion ◽  
Nonuniform Rotation ◽  
Drag Link ◽  
Space Occupation

Planar drag-link mechanism is a Grashofian four-bar chain with the shortest link fixed. In practice, the mechanism is used as a coupling between two shafts to convert uniform rotation of the driving shaft into a nonuniform rotation of the driven shaft. The nonuniformity in rotation is characterized by a cyclically increasing and decreasing delay (or advance) in the displacement of the driven shaft relative to that of the driving shaft. Drag-link synthesis problems include synthesizing the mechanism to generate a specified maximum delay. In a drag-link mechanism, the longer links make a full rotation about fixed pivots, which results in a relatively large installation space. This calls for designing drag-link mechanisms with a focus on space occupation, along with the traditional criteria of quality of motion transmission. Using position analysis, we investigate the relationships among mechanism space occupation, extreme transmission angle, and the generated maximum delay. Space occupation is represented by the link-length ratio of input link to fixed link. Given a desired maximum delay, the proposed approach suggests finding a unique extreme transmission angle value for which this link-length ratio is at a minimum. A closed-form solution to drag-link synthesis to generate a specified maximum delay is developed based on a compromise between quality of motion transmission and space occupation. For any drag-link designed by this compromise, the coupler link and the output crank are of the same length. Based on the obtained design equations, a graphical design solution and a method for evaluating space occupation are provided.

Computer-Based Kinematical Analysis of Spatial Multiloop Mechanisms

1992 ◽  
Author(s):  
Manfred Hiller ◽  
Manfred Möller
Keyword(s):  
Multibody System ◽  
Nonlinear Constraint ◽  
Constraint Equations ◽  
Revolute Joints ◽  
Spatial Mechanisms ◽  
Joint Coordinates ◽  
Prismatic Joints ◽  
Suitable Structure ◽  
Computer Based ◽  
Spatial Kinematics

Abstract In this paper a method for the automatical analysis of the kinematics of spatial multiloop mechanisms is presented. The mechanism is regarded as a multibody system. Connecting joints are revolute joints (R), prismatic joints (P), spherical joints (S) and all further joints that can be modelled as combinations of these joints. The concept allows the application for a user without deeper theoretical knowledge of spatial kinematics. Special effort has been taken in the reduction of the number of nonlinear constraint equations that must be solved. This is done by using an approach, yielding a suitable structure of the system of nonlinear constraint equations, where only those with interesting unknown joint coordinates must be solved. An optimized solution of these equations allows in many cases a partly and sometimes even a completely explicit solution of the constraint equations. The described method is also applicable to overconstrained spatial mechanisms.

Design of Drag-Link Mechanisms With Optimum Transmission Angle

1983 ◽  
Vol 105 (2) ◽  
pp. 254-258 ◽  
Author(s):  
Lung-Wen Tsai
Keyword(s):  
Extreme Values ◽  
Angular Displacement ◽  
Output Link ◽  
Link Length ◽  
Design Charts ◽  
Link Mechanism ◽  
Transmission Angle ◽  
New Criterion ◽  
Four Bar Linkage ◽  
Drag Link

In this paper, a new criterion for the design of a drag-link mechanism with optimum transmission angle is established. The transmission angle, the angle between the coupler link and output link of a four-bar linkage, is considered to be optimized when its extreme values deviate equally from 90 deg. Based on this criterion, design equations and design charts are developed. It is shown that the optimum drag-link mechanism is a turning-block linkage. It is also shown that to displace the drag-link mechanism with optimum transmission angle from its minimum lag to its maximum lag position, the input link must always rotate 180 deg and the corresponding angular displacement of the output link depends only on the link-length ratio of the output link to the fixed-link.

Kinematic Analysis and Design of 3-RPSR Parallel Mechanism with Triple Revolute Joints on the Base

2010 ◽  
Vol 4 (4) ◽  
pp. 346-354 ◽  
Author(s):  
Yukio Takeda ◽  
◽  
Xiao Xiao ◽  
Kazuya Hirose ◽  
Yoshiki Yoshida ◽  
...  
Keyword(s):  
Kinematic Analysis ◽  
Parallel Mechanism ◽  
Jacobian Matrix ◽  
Large Angle ◽  
Vertical Axis ◽  
Output Link ◽  
Analysis And Design ◽  
Revolute Joints ◽  
Full Rotation ◽  
Six Dof

The present paper proposes a new six-DOF parallel mechanism with three connecting chains. This mechanism can have a large angle of orientation of the output link. Joints in each connecting chain are arranged from the base in order of revolute, prismatic, spherical and revolute joints. All three revolute joints on the base are coaxial. With this structure, the output link can perform a full rotation around the vertical axis. The orientation capability of this mechanism is demonstrated. Equations for displacement analysis and the Jacobian matrix are derived. A design and prototype of this mechanism for a pipe-bender are shown.

Reconfiguration Analysis of Multimode Single-Loop Spatial Mechanisms Using Dual Quaternions

2017 ◽  
Vol 9 (5) ◽  
Author(s):  
Xianwen Kong
Keyword(s):  
Algebraic Geometry ◽  
Single Degree Of Freedom ◽  
Plane Symmetric ◽  
Dual Quaternions ◽  
Revolute Joints ◽  
Spatial Mechanisms ◽  
Reconfigurable Mechanisms ◽  
Motion Modes ◽  
Kinematic Loop ◽  
And Robotics

Although kinematic analysis of conventional mechanisms is a well-documented fundamental issue in mechanisms and robotics, the emerging reconfigurable mechanisms and robots pose new challenges in kinematics. One of the challenges is the reconfiguration analysis of multimode mechanisms, which refers to finding all the motion modes and the transition configurations of the multimode mechanisms. Recent advances in mathematics, especially algebraic geometry and numerical algebraic geometry, make it possible to develop an efficient method for the reconfiguration analysis of reconfigurable mechanisms and robots. This paper first presents a method for formulating a set of kinematic loop equations for mechanisms using dual quaternions. Using this approach, a set of kinematic loop equations of spatial mechanisms is composed of six polynomial equations. Then the reconfiguration analysis of a novel multimode single-degree-of-freedom (1DOF) 7R spatial mechanism is dealt with by solving the set of loop equations using tools from algebraic geometry. It is found that the 7R multimode mechanism has three motion modes, including a planar 4R mode, an orthogonal Bricard 6R mode, and a plane symmetric 6R mode. Three (or one) R (revolute) joints of the 7R multimode mechanism lose their DOF in its 4R (or 6R) motion modes. Unlike the 7R multimode mechanisms in the literature, the 7R multimode mechanism presented in this paper does not have a 7R mode in which all the seven R joints can move simultaneously.

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