Linkages That Transfer Rotations to Radially Reciprocating Motion

2010 ◽  
Author(s):  
Guowu Wei ◽  
Jian S. Dai
Keyword(s):  
Constraint Equation ◽  
Equation Method ◽  
Reciprocating Motion ◽  
Loop Equation ◽  
Revolute Joints ◽  
Kinematic Characteristics ◽  
Overconstrained Linkages ◽  
Geometry And Kinematics

Stemming from study of polyhedral and spheroidal linkages and investigation of reciprocating motion of the PRRP chain, this paper presents four overconstrained linkages that are capable of transferring rotations to radially reciprocating motion. The linkages connected by revolute joints are of symmetrical arrangement and mobility one and are analysed by using the screw-loop equation method. The paper further investigates geometry and kinematics of the linkages and reveals their kinematic characteristics, leading to the constraint equation.

Synthesis, Mobility, and Multifurcation of Deployable Polyhedral Mechanisms With Radially Reciprocating Motion

2014 ◽  
Vol 136 (9) ◽  
Author(s):  
Guowu Wei ◽  
Yao Chen ◽  
Jian S. Dai
Keyword(s):  
Geometric Constraints ◽  
Reciprocating Motion ◽  
Single Plane ◽  
Plane Symmetric ◽  
Loop Equation ◽  
Dual Plane ◽  
Potential Applications ◽  
Number Synthesis ◽  
First Time ◽  
Geometry And Kinematics

Extending the method coined virtual-center-based (VCB) for synthesizing a group of deployable platonic mechanisms with radially reciprocating motion by implanting dual-plane-symmetric 8-bar linkages into the platonic polyhedron bases, this paper proposes for the first time a more general single-plane-symmetric 8-bar linkage and applies it together with the dual-plane-symmetric 8-bar linkage to the synthesis of a family of one-degree of freedom (DOF) highly overconstrained deployable polyhedral mechanisms (DPMs) with radially reciprocating motion. The two 8-bar linkages are compared, and geometry and kinematics of the single-plane-symmetric 8-bar linkage are investigated providing geometric constraints for synthesizing the DPMs. Based on synthesis of the regular DPMs, synthesis of semiregular and Johnson DPMs is implemented, which is illustrated by the synthesis and construction of a deployable rectangular prismatic mechanism and a truncated icosahedral (C60) mechanism. Geometric parameters and number synthesis of typical semiregular and Johnson DPMs based on the Archimedean polyhedrons, prisms and Johnson polyhedrons are presented. Further, movability of the mechanisms is evaluated using symmetry-extended rule, and mobility of the mechanisms is verified with screw-loop equation method; in addition, degree of overconstraint of the mechanisms is investigated by combining the Euler's formula for polyhedrons and the Grübler–Kutzbach formula for mobility analysis of linkages. Ultimately, singular configurations of the mechanisms are revealed and multifurcation of the DPMs is identified. The paper hence presents an intuitive and efficient approach for synthesizing PDMs that have great potential applications in the fields of architecture, manufacturing, robotics, space exploration, and molecule research.

Mobility and Geometric Analysis of the Hoberman Switch-Pitch Ball and Its Variant

2010 ◽  
Vol 2 (3) ◽  
Author(s):  
Guowu Wei ◽  
Xilun Ding ◽  
Jian S. Dai
Keyword(s):  
Geometric Analysis ◽  
Loop Equation ◽  
Bevel Gears ◽  
Kinematic Characteristics ◽  
Special Case ◽  
Geometry And Kinematics

This paper investigates the mobility and kinematics of the Hoberman switch-pitch ball, and particularly, its variant that does not resort to bevel gears. The ball variant is a general case of the Hoberman switch-pitch ball and constitutes the ball. This paper starts from examining the geometry of the ball variant and its composition, and decomposes it into loops containing eight-bar radially foldable linkages. To investigate the eight-bar radially foldable linkage, constraint matrices are developed using the screw-loop equation. This paper extends the study to the ball variant and investigates the singularity and various configurations based on the geometry and kinematics of the ball variant. This leads to the investigation of the Hoberman switch-pitch ball as a special case of the ball variant with bevel gears to simultaneously drive three joints in every vertex of the ball mechanism. The analysis is then followed by a numerical demonstration of the kinematic characteristics of the Hoberman switch-pitch ball.

Synthesis and Construction of a Family of One-DOF Highly Overconstrained Deployable Polyhedral Mechanisms (DPMs)

2012 ◽  
Author(s):  
Guowu Wei ◽  
Jian Dai
Keyword(s):  
Equation Method ◽  
Reciprocating Motion ◽  
Mobility Analysis ◽  
Plane Symmetric ◽  
Kinematic Chains ◽  
Loop Equation ◽  
Euler’S Formula ◽  
The Family

This paper presents a family of one-DOF highly overconstrained regular and semi-regular deployable polyhedral mechanisms (DPMs) that perform radially reciprocating motion. Based on two fundamental kinematic chains with radially reciprocating motion, i.e. the PRRP chain and a novel plane/semi-plane-symmetric spatial eight-bar linkage, two methods, i.e. the virtual-axis-based (VAB) method and the virtual-centre-based (VCB) method are proposed for the synthesis of the family of regular and semi-regular DPMs. Procedure and principle for synthesizing the mechanisms are presented and selected DPMs are constructed based on the five regular Platonic polyhedrons and the semi-regular Archimedean polyhedrons, Prism polyhedrons and Johnson polyhedrons. Mobility of the mechanisms is then analysed and verified using screw-loop equation method and degree of overconstraint of the mechanisms are investigated by combing the Euler’s formula for polyhedrons and the Grübler-Kutzbach formula for mobility analysis of linkages.

Geometric and Kinematic Analysis of the Hoberman Switch-Pitch Ball and Its Variant

2009 ◽  
Author(s):  
Guowu Wei ◽  
Xilun Ding ◽  
Jian S. Dai
Keyword(s):  
Kinematic Analysis ◽  
Numerical Example ◽  
Bevel Gears ◽  
Kinematic Characteristics ◽  
Special Case ◽  
Geometry And Kinematics

This paper investigates geometry and kinematics of the Hoberman switch-pitch ball and its variant as an extended case of the ball. The paper starts from examining the geometry of the ball variant and its composition and decomposes it into loops each of which is an eight-bar radial linkage. Based on this, the paper investigates the geometry of the eight-bar radial linkage and the variant and subsequently extends the study to their kinematics. The Hoberman switch-pitch ball as a special case of the ball variant with bevel gears is investigated and a numerical example is employed to illustrate the kinematic characteristics of the eight-bar radial linkage and the Hoberman switch-pitch ball.

Railway Vehicle Modelling by the Constraint Equation Method∗

1984 ◽  
Vol 13 (5) ◽  
pp. 281-297 ◽  
Author(s):  
Luis M. Martin ◽  
José G. Giménez
Keyword(s):  
Constraint Equation ◽  
Equation Method ◽  
Railway Vehicle

Measurement of Cutting Speed of Mechanical Excavator

2014 ◽  
Vol 538 ◽  
pp. 331-334
Author(s):  
Ya Juan Hou ◽  
Ji Sheng Wang ◽  
Ai Feng Li ◽  
Su He Gao ◽  
Guo Qiang Wang
Keyword(s):  
Theoretical Result ◽  
Cutting Speed ◽  
Logarithmic Spiral ◽  
Constraint Equation ◽  
Virtual Prototype ◽  
Equation Method ◽  
Analytical Expression ◽  
Spiral Trajectory ◽  
High Efficient ◽  
Cooperative Relationship

Only when mining at reasonable cutting speed, can a mechanical excavator achieve high efficient and low consumption. The same cutting-angle logarithmic spiral trajectory is initially confirmed for the model of a reasonable excavating trajectory to reduce digging resistance. An analytical expression between hoisting and pushing speed is derived from the mechanism kinematics theory and the constraint equation method. This expression accurately describes the cooperative relationship between these speeds. Virtual prototype kinematics of a large mechanical excavator are simulated and verified through ADAMS. The simulation result is consistent with the theoretical result, and thus validates the analytical expression between hoisting and pushing speed.

A Spatial Eight-Bar Linkage and Its Association With the Deployable Platonic Mechanisms

2014 ◽  
Vol 6 (2) ◽  
Author(s):  
Guowu Wei ◽  
Jian S. Dai
Keyword(s):  
Closed Form ◽  
Degrees Of Freedom ◽  
Structure Parameters ◽  
Reciprocating Motion ◽  
Motion Feature ◽  
Plane Symmetric ◽  
Dual Plane ◽  
Straight Line ◽  
First Time ◽  
Geometry And Kinematics

This paper presents for the first time a novel two degrees of freedom (2-DOF) single-looped dual-plane-symmetric spatial eight-bar linkage with exact straight-line motion. Geometry and kinematics of the eight-bar linkage are investigated and closed-form equations are presented revealing the exact straight-line motion feature of the linkage on the condition that two symmetric inputs are given. In order to secure two symmetric inputs, a geared eight-bar linkage is then proposed converting the linkage into a 1-DOF linkage of exact straight-line motion. The direction of the straight-line motion produced by the proposed eight-bar linkage is changeable and is only dependent on the structure parameters of the two pairs of V-shaped R-R dyads of the linkage. Further, the proposed eight-bar linkage is applied to the synthesis and construction of a group of deployable Platonic mechanisms with radially reciprocating motion. The virtual-center-based (VCB) method is presented for the synthesis and prototypes of the deployable Platonic mechanisms are fabricated verifying the mobility and motion of the proposed mechanisms.

KINEMATIC FEATURES OF THE LAPPING PROCESS AND DETERMINATION OF ITS BASIC PARAMETERS

2020 ◽  
Vol 7 (3) ◽  
pp. 23-28
Author(s):  
EZIZ SARVAN SHIRVAN ◽  
Keyword(s):  
Dynamic Properties ◽  
Cutting Speed ◽  
Equilibrium System ◽  
Technological Parameters ◽  
Kinematic Characteristics ◽  
Angular Velocities ◽  
Basic Parameters ◽  
Grinding Tool ◽  
Mathematical Relationships ◽  
Analytical Expressions

This paper discusses the kinematic characteristics of lapping process and the main parameters of the process. It was determined that the influencing degree of technological parameters to the forming surface and processes. It was projected the construction of the lapping head for processing of internal cylindrical surfaces, scheme of the lapping operation and graphic description of the forces influencing. The relationships between the axial, radial and tangential cutting forces and the effect of the combined force thereof are determined in order to ensure the necessary surface pressure. During the analysis geometric and mathematical relationships were obtained. The extracted analytical expressions can be realized by further experimental researches and can be used in engineering calculations of technological parameters of processing by lapping. Angular velocity, friction force, linear velocity, also the length of the tactile curve and the radius of the part can be considered the main kinematic and dynamic parameters of the process that the formation of the surface, also the course of the process depends on these parameters. Depending on the kinematic parameters, the wear nature of the tool changes and this changes the linear and angular velocities, which have a significant impact on the accuracy, quality and productivity of processing. When examining the technological capabilities of the process, the nature of the movement between the part and the grinding tool, also changes in cutting speed are often considered as a main factor. Analytical expressions were obtained to determine the main parameters of the process, taking into account the kinematic characteristics of the friction process. These expressions can be used in engineering calculations and allow to determine the optimal values of the processing mode. In order to obtain the required micrometric surface cleanliness and measurement accuracy, correlation relationships were established between the main parameters of the process, equations of the equilibrium system of shear forces were compiled and analytical expressions were obtained based on the analysis of kinematic and dynamic properties of the system.

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