Kinematics Of Serial Manipulators Research Articles

Geometry and Direct Kinematics to MP3R with 444 Operators

Anthropomorphic mechatronic systems are the most widely used robotics systems worldwide today in industry and in all automated environments. These systems are best suited to the modern automation and mechatronisation needs of the modern world, being mobile, dynamic, light, robust, complex, technologically simple, easy to design and manufactured, implemented, maintained and used in almost any industrial site, both in machine building and in special environments, such as chemical, toxic, dyeing, underwater, nuclear, in space.... Anthropomorphic robots are flexible, dynamic, stable, lightweight, fast, fast, inexpensive, easy-to-install, mechanical, mechanical, mechanical and mechanical systems with a pleasant appearance, modern industrial design and easy to design and implement in any workplace, imposed. In this study we will present the 4×4 operators and the way they can be implemented and used in the complex matrix calculations in order to simplify the complex matrix algebraic numerical methods. 4×4 operators are designed to simplify algebraic matrix calculations by making difficult matrix operations simpler and easier to approach. The method of using 4×4 operators is meant to introduce a degree in addition to the matrices to facilitate algebraic operations. The kinematics of serial manipulators and robots will be exemplified for the 3R kinematic model. The fixed coordinate system was denoted by x0O0y0z0. The mobile systems (rigid) of the three mobile elements (1, 2, 3) have indices 1, 2 and 3. Their orientation has been chosen conveniently. Known kinematic parameters in the direct kinematics are the absolute rotation angles of the three moving elements: φ10, φ20, φ30, angles related to the rotation of the three actuators (electric motors) mounted in the kinematic rotation couplers. The output parameters are the three absolute coordinates xM, yM, zM of point M, i.e., the kinematic parameters (coordinates) of the endeffector (the actuator element (the final), which can be a grasping hand, a solder tip, painted , cut, etc ...). The 3×3 matrix is transformed into 4×4 (it is a mathematical operator) by adding two zero vectors (formed from three elements 0), one line and the other column, and adding one element 1 to the main diagonal (the last element). The matched T01 matrix becomes T014. The column vector matrix (consisting of three elements) undergoes a minimal transformation receiving a fourth fixed value 1 if it is only used for matrix products. The convenient form of matrix A12 is A12c.

Geometry and Direct Kinematics to MP3R with 4×4 Operators

Anthropomorphic mechatronic systems are the most widely used robotics systems worldwide today in industry and in all automated environments. These systems are best suited to the modern automation and mechatronisation needs of the modern world, being mobile, dynamic, light, robust, complex, technologically simple, easy to design and manufactured, implemented, maintained and used in almost any industrial site, both in machine building and in special environments, such as chemical, toxic, dyeing, underwater, nuclear, in space.... Anthropomorphic robots are flexible, dynamic, stable, lightweight, fast, fast, inexpensive, easy-to-install, mechanical, mechanical, mechanical and mechanical systems with a pleasant appearance, modern industrial design and easy to design and implement in any workplace, imposed. In this study we will present the 4×4 operators and the way they can be implemented and used in the complex matrix calculations in order to simplify the complex matrix algebraic numerical methods. 4×4 operators are designed to simplify algebraic matrix calculations by making difficult matrix operations simpler and easier to approach. The method of using 4×4 operators is meant to introduce a degree in addition to the matrices to facilitate algebraic operations. The kinematics of serial manipulators and robots will be exemplified for the 3R kinematic model. The fixed coordinate system was denoted by x0O0y0z0. The mobile systems (rigid) of the three mobile elements (1, 2, 3) have indices 1, 2 and 3. Their orientation has been chosen conveniently. Known kinematic parameters in the direct kinematics are the absolute rotation angles of the three moving elements: φ10, φ20, φ30, angles related to the rotation of the three actuators (electric motors) mounted in the kinematic rotation couplers. The output parameters are the three absolute coordinates xM, yM, zM of point M, i.e., the kinematic parameters (coordinates) of the endeffector (the actuator element (the final), which can be a grasping hand, a solder tip, painted , cut, etc ...). The 3×3 matrix is transformed into 4×4 (it is a mathematical operator) by adding two zero vectors (formed from three elements 0), one line and the other column, and adding one element 1 to the main diagonal (the last element). The matched T01 matrix becomes T014. The column vector matrix (consisting of three elements) undergoes a minimal transformation receiving a fourth fixed value 1 if it is only used for matrix products. The convenient form of matrix A12 is A12c.

Direct Geometry and Cinematic to the MP-3R Systems

Mechatronic robotic systems are today widely used worldwide to ease human work, but especially where work is dangerous, in toxic, radioactive, chemical, explosive atmospheres, without air such as underwater or in the cosmos, or in places hard to reach the man. Robots can take the tedious repetitive work under any circumstances and they can perform a difficult operation for a long time, with no meal or rest breaks. They say the robots have stolen people's jobs. False! Robots have taken from man only those difficult jobs that baptized man and destroyed him. Robots have been created just as a prolongation of man as his real support in the faster, constantly accomplishing of difficult, repetitive, physically and mentally tired work and operations. Robots have emerged many years ago as a requirement of the automotive industry and especially that of road vehicles, especially automobiles. Meanwhile, they have diversified and branched a great deal in almost all industrial spheres. But the most important future of robots must be completely different. They have to help us conquer the cosmic space. The robot must become an extension of man in his divine mission of constructor and conqueror of the universe. Of all the types of industrial robots you use, the most common are the anthropomorphic serial robots, which is why we want to start studying and presenting the robots, with that generally common in robots, anthropomorphic serial systems. The kinematics of serial manipulators and robots will be exemplified for the 3R cinematic model to a medium difficulty system, ideal for understanding the actual phenomenon, but also for explaining the basic knowledge needed for calculating calculations and simpler or more complex systems. The fixed coordinate system was denoted by x0O0y0z0. The mobile systems (rigid) of the three mobile elements (1, 2, 3) have indices 1, 2 and 3. Their orientation was conveniently chosen but other orientations could be chosen. Known kinematic parameters in the direct kinematics are the absolute rotation angles of the three moving elements: φ10, φ20, φ30, angles related to the rotation of the three actuators (electric motors) mounted in the kinematic rotation couplers. The output parameters are the three absolute coordinates xM, yM, zM of point M, ie the kinematic parameters (coordinates) of the end-effector (the actuator element (the final), which can be a grasping hand, a solder tip, painted , cut, etc ...).