Speeds and Accelerations in Direct Kinematics to the MP3R Systems

Corresponding Author: Florian Ion Tiberiu Petrescu ARoTMM-IFToMM, Bucharest Polytechnic University, Bucharest, (CE), Romania E-mail: scipub02@gmail.com Abstract: Today, robots and mechatronic systems are constantly playing an essential role in our lives, being a key link in the automotive industry, without which it can no longer be conceived. If the robots initially started in the machine building industry to the imperious demands of the car king to have a growing production fast and steadily, helping the logarithmic progression of automotive construction, today robots and automation have rapidly penetrated all areas of the machine building industry, due to their ability to produce fast, long, quality, without pauses, country illnesses, at an innate pace, far outweighing man in this chapter. Additionally, robots can work in toxic, dangerous, airless environments, such as in space or underwater, at high pressures, or in potentially dangerous places. There is no question of removing robots from industrial work today. On the contrary, there is a fierce competition in the acquisition, construction, implementation and maintenance of as many robotic mechanical systems due to their high working capacity but also because they have a high reliability and a high quality of the operations performed. In this study we will treat the kinematicity of anthropomorphic robots, as they are today the most widespread robots in the global industry, due to their huge work capabilities and rapid adaptation to any working conditions. It will highlight the speeds and accelerations of these moving mechanical systems in direct kinematics.


Introduction
The humanoids robots are used now as a tool for research in several scientific fields.
Researchers need to understand the structure of the human body and behavior (biomechanics) to build and to study robots humanoids. On the other hand, the attempt simulation of the human body leads to a greater understanding of it. Human knowledge is a field of study, which is focused on the way in that people learn from sensory information in order to acquire the skills and insightful motor. Such knowledge are used to develop models for the calculation of human behavior and have been improved in time.
It has been suggested that robotics highly advanced will facilitate its increase even in ordinary people.
With all that the original purpose of humanoid research has been to build a better orthosis and prosthesis for human beings, knowledge has been transferred between the two disciplines. Some examples are Prosthesis footswitch with electrical adjustment for impaired neuromuscular, orthosis ankle-foot, biological realistic prosthesis leg and forearm prosthesis (Aversa et al., 2017a-e;2016a-o).
In addition to the research, robots humanoids are developed to perform human activities, such as personal assistance, where they would be able to help places of work diseased and the elderly and dirty or dangerous.
Workplaces ordinary, such as to be a yacht or a worker of a production line of cars are also suitable for the humanoids." In essence, as they can use tools and operate the equipment and vehicles designed to human form, those humanoids could carry out, theoretically, any load a human being may, as long as they have the software itself. However, the complexity to do this is deceptively big.
Today, robots and mechatronic systems are constantly playing an essential role in our lives, being a key link in the automotive industry, without which it can no longer be conceived. If the robots initially started in the machine building industry to the imperious demands of the car king to have a growing production fast and steadily, helping the logarithmic progression of automotive construction, today robots and automation have rapidly penetrated all areas of the machine building industry, due to their ability to produce fast, long, quality, without pauses, country illnesses, at an innate pace, far outweighing man in this chapter.
Additionally, robots can work in toxic, dangerous, airless environments, such as in space or underwater, at high pressures, or in potentially dangerous places.
There is no question of removing robots from industrial work today. On the contrary, there is a fierce competition in the acquisition, construction, implementation and maintenance of as many robotic mechanical systems due to their high working capacity but also because they have a high reliability and a high quality of the operations performed.
In this study we will treat the kinematicity of anthropomorphic robots, as they are today the most widespread robots in the global industry, due to their huge work capabilities and rapid adaptation to any working conditions. It will highlight the speeds and accelerations of these moving mechanical systems in direct kinematics.
Today the moving mechanical systems are utilized in almost all vital sectors of humanity (Reddy et al., 2012). The robots are able to process integrated circuits (Aldana et al., 2013) sizes micro and nano, on which the man they can be seen only with electron microscopy (Lee, 2013). Dyeing parts in toxic environments, working in chemical and radioactive environments (Padula and Perdereau, 2013;Perumaal and Jawahar, 2013), or at depths and pressures at the deep bottom of huge oceans, or conquest of cosmic space and visiting some new exoplanets, are with robots systems possible (Dong et al., 2013) and were turned into from the dream in reality (Garcia et al., 2007), because of use of mechanical platforms sequential gearbox Petrescu et al., 2009). The man will be able to carry out its mission supreme (Tang et al., 2013;Tong et al., 2013), conqueror of new galaxies (de Melo et al., 2012), because of mechanical systems sequential gearbox (robotics systems) (Garcia-Murillo et al., 2013).
Robots were developed and diversified (Lin et al., 2013), different aspects (He et al., 2013), but today, they start to be directed on two major categories: systems serial (Liu et al., 2013;Petrescu and Petrescu, 2011b) and parallel systems . Parallel systems are more solid (Tabaković et al., 2013;Wang et al., 2013) but more difficult to designed and handled and for this reason, the serial systems were those which have developed the most. In medical operations or radioactive environments are preferred mobile systems parallel, because of their high accuracy positioning.

X A T X A T A T X A T A T T X A T A T T A T X A T A T T A T T T X
This is written in simplified form (2): Where: Matrix relation (2) Because: Next, determine the two matrix products (15 and 16) of relation (8).
We can now determine 0M X ɺ :

Results
Follows, the acceleration relations. The relationship (8) is derived and the expression (18) The fairly simple form of the matrix 12 P ɺɺ is due to the fact that the three angular speeds of the actuators were considered constant (as is normal).    2  2  10  10  10  10   2  2  03  3  10  10  10  10   2  3  10  10  30  3  30  2  3  30  3  10  10 The matrix of the impedance acceleration matrices is obtained according to the rotations and angular speeds of the three actuators, with ω 10 = ct, ω 20 = ct, ω 30 = ct.

Discussion
Today, robots and mechatronic systems are constantly playing an essential role in our lives, being a key link in the automotive industry, without which it can no longer be conceived. If the robots initially started in the machine building industry to the imperious demands of the car king to have a growing production fast and steadily, helping the logarithmic progression of automotive construction, today robots and automation have rapidly penetrated all areas of the machine building industry, due to their ability to produce fast, long, quality, without pauses, country illnesses, at an innate pace, far outweighing man in this chapter. Additionally, robots can work in toxic, dangerous, airless environments, such as in space or underwater, at high pressures, or in potentially dangerous places. There is no question of removing robots from industrial work today. On the contrary, there is a fierce competition in the acquisition, construction, implementation and maintenance of as many robotic mechanical systems due to their high working capacity but also because they have a high reliability and a high quality of the operations performed. In this study, we will treat the kinematics of anthropomorphic robots, as they are today the most widespread robots in the global industry, due to their huge work capabilities and rapid adaptation to any working conditions. It will highlight the speeds and accelerations of these moving mechanical systems in direct kinematics.

Conclusion
Serial, mechanical and mobile systems have rapidly and steadily penetrated almost all industrial areas due to their flexibility, reliability, simple implementation and adaptability to various types of mechanical machining in the automotive industry. In addition, they occupy less space and volume compared to parallel systems and are easier to manufacture and implement, but also much cheaper. Serial systems have been noticed since the beginnings of robotics and mechatronics due to their flexibility, their work dynamics and the dynamics of their implementation. In addition, there are useful, reliable systems with high efficiency and productivity, economic and industrial.
The paper presents an exact, original analytical method for determining the direct kinematic parameters of a serial mobile structure.

Acknowledgment
This text was acknowledged and appreciated by Dr. Veturia CHIROIU Honorific member of Technical Sciences Academy of Romania (ASTR) PhD supervisor in Mechanical Engineering and by Prof. BERTHOLD GRUNWALD, Past Director Mercedes Benz Daimler AG, Germany and Past Head Department of Automotive Engineering from Bucharest Polytechnic University, whom we thank and in this way.

Funding Information
Research contract: Contract number 36-5-4D/1986 from 24IV1985, beneficiary CNST RO (Romanian National Center for Science and Technology) Improving dynamic mechanisms.
Contract research integration. 19-91-3 from 29.03.1991; Beneficiary: MIS; TOPIC: Research on designing mechanisms with bars, cams and gears, with application in industrial robots.
Contract research. GR 69/10.05.2007: NURC in 2762; theme 8: Dynamic analysis of mechanisms and manipulators with bars and gears.