Geometry Modeling for Indexing Cams Based on Screw Theory and Product of Exponential Formula

2006 ◽  
Vol 505-507 ◽  
pp. 991-996
Author(s):  
Zong Yu Chang ◽  
Yu Hu Yang ◽  
Ce Zhang ◽  
Shou Bin Ding ◽  
Bin Zhang ◽  
...  
Keyword(s):  
Kinematic Analysis ◽  
Screw Theory ◽  
Product Formula ◽  
Coordinate Systems ◽  
Model Surface ◽  
Cam Mechanism ◽  
Geometry Modeling ◽  
Exponential Formula ◽  
Indexing Mechanism ◽  
Systems Transformation

This paper proposes a method of geometry modeling for indexing cam mechanism by using screw theory and exponential product formula. Kinematic analysis based on screw theory is introduced firstly. Then, method to model surface of indexing cams is presented when screw theory and exponential product formula are applied. The paper gives examples to obtain the geometry models of roller gear cam, barrel indexing cam and parallel indexing cam. Our work suggests that this method can avoid the burdensome work on building coordinate systems, transformation matrixes and understanding on the mechanism. Moreover, this method can be used to innovate and design new types of indexing mechanism.

Research and Application on a Multi Head Conjugate Disc Indexing Cam Mechanism

2012 ◽  
Vol 184-185 ◽  
pp. 384-388
Author(s):  
Bing Tian Gao
Keyword(s):  
High Speed ◽  
Production Efficiency ◽  
High Reliability ◽  
Low Cost ◽  
Domestic Industry ◽  
Cam Mechanism ◽  
Technical Performance ◽  
Working Performance ◽  
Research Achievement ◽  
Indexing Mechanism

In order to realize the technical performance of high speed, high precision, high stability and high reliability for conjugated indexing mechanism with periodic intermittent rotary motion, a two cams structure has been designed, and its geometry size and profile curve was carefully determined. Also the calculation formula of the contour curve for CAM was deduced. Research achievement has been applied to new equipment of enterprise development, the working performance is stable and reliable, the production efficiency raised by 30% compared to the domestic industry. The mechanism has characteristics of simplified structure, improved transmission performance and low cost.

Application Research on a Curved CAM Surface Reconstruction Method

2014 ◽  
Vol 971-973 ◽  
pp. 402-405
Author(s):  
Zhou Wen ◽  
Jun Ling Zhang ◽  
Xiu Duan Gong
Keyword(s):  
Reverse Engineering ◽  
Surface Reconstruction ◽  
Design Method ◽  
Subsequent Development ◽  
Reconstruction Method ◽  
Application Research ◽  
Cam Mechanism ◽  
Indexing Mechanism ◽  
Contour Surface ◽  
Rapid Modeling

Globular indexing CAM mechanism is a good indexing mechanism. As the working curve of CAM contour surface is no extending curved surface, there is certain difficulty to design processing. It is new kinds of design method that reverse engineering apply in rapid modeling of curved CAM. In this way, designer can complete curve of CAM reverse modeling, and the rationality of the model is verified. At the same time, it also can reverse modeling and the subsequent development of other products to provide a reference.

Study on the compound transmission mechanism of the curve-face gear based on screw theory

2017 ◽  
Vol 232 (17) ◽  
pp. 3115-3124 ◽  
Author(s):  
Chao Lin ◽  
Yanqun Wei ◽  
Zhiqin Cai
Keyword(s):  
Screw Theory ◽  
Transmission Mechanism ◽  
Tooth Surface ◽  
Design Parameters ◽  
Gear Pair ◽  
Face Gear ◽  
Cylindrical Gear ◽  
Cam Mechanism ◽  
Conjugate Surfaces ◽  
Curve Face

The compound transmission mechanism of curve-face gear is a new type of gear transmission based on the cam mechanism and the curve-face gear pair. It combines the transmission characteristics of the cam mechanism and noncircular bevel gear. When the compound transmission mechanism of curve-face gear is engaged in the meshing transmission, the rotating center of the cylindrical gear is fixed and used as the driving wheel, and the curve-face gear can generate the helical motion around the axis. In this paper, the meshing characteristics and motion laws of the compound transmission mechanism of the curve-face gear are studied based on the theory of screw. Based on the meshing theory of gears, the coordinate system of conjugate surfaces is established, the basic meshing theory and equation are obtained. On this basis, combined with the principle of the cam, the transmission principle is analyzed by the screw theory. The tooth surface equation of the compound transmission mechanism of curve-face gear is deduced based on the meshing theory and the related knowledge of geometry. The motion law of the curve-face gear and the change of the motion law with the change of the basic parameters of the gear pair with different design parameters are calculated and analyzed. An experimental platform is built to verify the law of motion, and the experimental results are compared with the theoretical values. The correctness of the theoretical analysis is verified, which provides a new way for the research of the compound transmission mechanism of the curve-face gear.

Identification of principal screws of two- and three-screw systems

2007 ◽  
Vol 221 (12) ◽  
pp. 1701-1715 ◽  
Author(s):  
J-S Zhao ◽  
F Chu ◽  
Z-J Feng
Keyword(s):  
Screw Theory ◽  
Coordinate Systems ◽  
Third Order ◽  
Analytical Methodology ◽  
Partial Derivatives ◽  
Spatial Mechanisms ◽  
Analysis Theory ◽  
Definition Of ◽  
Derivatives Of ◽  
Homogeneous Linear

The current paper proposes a unified analytical methodology to identify the principal screws of two- and three-screw systems. Based on the definition of the pitch of a screw, it first obtains an identical homogeneous quadric equation. According to functional analysis theory, it is known that the partial derivatives of an identical quadric equation with respect to its variables must be zero. Therefore, the paper deduces a set of linear homogeneous equations that are made up of the partial derivatives of the quadric equation. With the existing criteria of non-zero solutions for homogeneous linear algebra equations, it ultimately obtains the formulas of the principal pitches and the associated principal screws of the system. The most outstanding contribution of this methodology is that it proposes a unified analytical approach to identify the principal pitches and the principal coordinate systems of the second-order and the third-order screw systems. This should be a new contribution to the screw theory and will boost its applications to the kinematics analysis of robots and spatial mechanisms.

scholarly journals Trajectory Planning Based on Screw Theory with Consideration of the Optimal Berth Position for a Space Robot

2019 ◽  
Vol 2019 ◽  
pp. 1-14
Author(s):  
Yong Wang ◽  
Ying Liao ◽  
Kejie Gong
Keyword(s):  
Trajectory Planning ◽  
Screw Theory ◽  
Optimization Method ◽  
Euler Method ◽  
Space Robot ◽  
Optimization Strategy ◽  
Generalized Jacobian ◽  
End Effector ◽  
Planning Strategy ◽  
Exponential Formula

Trajectory planning is a prerequisite for the tracking control of a free-floating space robot. There are usually multiple planning objectives, such as the pose of the end-effector and the base attitude. In efforts to achieve these goals, joint variables are often taken as exclusive operable parameters, while the berth position is neglected. This paper provides a novel trajectory planning strategy that considers the berth position by applying screw theory and an optimization method. First, kinematic equations at the position level are established on the basis of the product of exponential formula and the conservation of the linear momentum of the system. Then, generalized Jacobian matrices of the base and end-effector are derived separately. According to the differential relationship, an ordinary differential equation for the base attitude is established, and it is solved by the modified Euler method. With these sufficient and necessary preconditions, a parametric optimization strategy is proposed for two trajectory planning cases: zero attitude disturbance and attitude adjustment of the base. First, the berth position is transformed into the desired position of the end-effector, and its constraints are described. Joint variables are parameterized using a sinusoidal function combined with a five-order polynomial function. Then, objective functions are constructed. Finally, a genetic algorithm with a modified mutation operator is used to solve this optimization problem. The optimal berth position and optimized trajectory are obtained synchronously. The simulation of a planar dual-link space robot demonstrates that the proposed strategy is feasible, concise, and efficient.

The Algorithm of Redundant Robotic Kinematics Based on Exponential Product

2011 ◽  
Vol 58-60 ◽  
pp. 1902-1907 ◽  
Author(s):  
Xin Fen Ge ◽  
Jing Tao Jin
Keyword(s):  
Real Time ◽  
Inverse Kinematics ◽  
Screw Theory ◽  
Product Formula ◽  
Real Time Control ◽  
Time Control ◽  
Direct Kinematics ◽  
Product Formulas

The intrinsically redundant series manipulator’s kinematics were studied by the exponential product formula of screw theory, the direct kinematics problem and Inverse kinematics problems were analyzed, and the intrinsically redundant series manipulator’s kinematics solution that based on exponential product formulas were proposed; the intrinsically redundant series manipulator’s kinematics is decomposed into several simple sub-problems, then analyzed sub-problem, and set an example to validate the correctness of the proposed method. Finally, comparing the exponential product formula and the D-H parameters, draw that they are essentially the same in solving the manipulator’s kinematics, so as to the algorithm of the manipulator’s kinematics based on exponential product formulas are correct, and the manipulator’s kinematics process based on exponential product formula is more simple and easier to real-time control of industrial.

An application of screw theory to the kinematic analysis of a Delta-type robot

2014 ◽  
Vol 28 (9) ◽  
pp. 3785-3792 ◽  
Author(s):  
Jaime Gallardo-Alvarado ◽  
Albert L. Balmaceda-Santamaría ◽  
Eduardo Castillo-Castaneda
Keyword(s):  
Kinematic Analysis ◽  
Screw Theory ◽  
Delta Type
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