Introduction To Robotics 2e – Sk Saha

For a revolute joint, the actuator exerts a torque about the ith joint axis. Assuming that frictional torque at the joint is negligible, the actuator force ti is given by ti = ei T ni–1, i (7.13) where ei is the unit vector pointing along the positive ith joint axis, i.e., Zi of Fig. 7.1, about which the relative motions between the two neighboring links take place. The actuator torque has that component of ni–1,i which is corresponding to the direction of the joint axis. Its other two components are reactions that are to be supported by the joint bearing.

The term ti is called the joint torque. For a prismatic joint, the actuator force is similarly obtained. It is the force exerted along the ith joint axis. Again, assuming that frictional force at the joint is negligible, the actuator force denoted with the same letter ti, is expressed as ti = ei T fi–1, i (7.14) where ei is the unit vector pointing along the positive ith joint axis along which the two neighboring links translate.

Equation (7.14) implies that the actuator force only bears the component of fi–1 i along the direction of the joint axis, while its other two components are supported by the joint bearings. Using the 6-dimensional wrench notation wi–1, i the joint force or torque ti can be written as ti = pi T wi–1, i (7.15) where pi is the 6-dimensional joint-motion propagation vector for the revolute or prismatic joint, as the case may be which are given in Eqs. (6.94b) or (6.96), respectively. Statics of a Two-link Planar Arm Example 7.1 The two-link planar manipulator arm is applying a force f on the environment, say, a wall, with its end-effector.

Assume that the force f is known in the end-effector frame, i.e., in frame 3. Hence, [f23]3 ∫ [fx, fy, 0]T. The required joint torques are found as a function of the arm confi gurations and the applied force components. Note that the gravity does not play any role when the manipulator is lying on the horizontal plane.

Referring to Fig. 7.2 and Eqs. (7.9–7.10), [f23]3 ∫ ; and 12 2 23 3 [ ] [ ] y y y f c f s f f f s f c – ˘ ˘ ˙ ˙ = = + ˙ ˙ ˙ ˙ ˚ ˚ f Q f (7.16a) where the orientation matrix Q2 is given by s s – ˘ ˙ ˙ ˙ ˚ (7.16b) In Eqs.

(7.16a-b), s2 and c2 respectively represent sin q2 and cos q2. Statics and Manipulator Design Fig.

Born in Malda, West Bengal (India), Subir Kumar Saha completed most of his school studies from Vidyasagar Vidyapith, Midnapore (also in West Bengal). He obtained a BE (Mech.) from RE College (now NIT), Durgapur in 1983, followed by a Master’s from IIT Kharagpur in 1985. He then obtained a PhD degree from McGill University, Canada, in 1991, and immediately joined the R&D Center of Toshiba Corporation in Japan. At Toshiba, he worked on space robot dynamics. In 1995, he returned to IIT Madras as a Visiting Faculty, before joining IIT Delhi in 1996 as an Assistant Professor.

Since 2006 he is a Professor at IIT Delhi, and presently he holds the Naren Gupta Chair Professorship at IIT Delhi. Prof. Saha is in the Dean’s Honors’ List of McGill University for his Excellent PhD thesis, and received the Humboldt Fellowship during 1999-2000 when he was at the University of Stuttgart, Germany. He has also been a visiting faculty/researcher to several universities abroad, for example, McGill University, Canada, Monash University, Australia, University of Verona, Italy, and Waseda-IPS, Japan.

Prof. Saha is actively engaged in teaching, research, and technology development. His present book’s (Introduction to Robotics) fi rst edition was widely acclaimed by readers in India and abroad. The RoboAnalyzer software (http://www.roboanalyzer.com) that complements the book was also well received and is very popular. He established the SAE-IIT Delhi Chapter in 1997, Robotics Club in 2002, Mechatronics Laboratory in July 2001, and contributed signifi cantly in setting up the Programme for Autonomous Robotics (PAR) Laboratory in May 2010.

His research, consultancy, and training activities with many private companies like Asahi India, Sona Steering, Minda-Huf, SAMTEL Colour Tubes, and public sectors like BHEL, CEPC, and government agencies like DST, MIT, CWDB, Simulator Development Division, BARC/BRNS are clear indicators of the industries’ confi dence in Prof. Saha’s commitment. Prof. Saha has more than 185 research publications in reputed journals and conference proceedings, and has delivered more than 160 invited lectures. Two of Prof. Saha’s special interests are (1) popularizing the concept of engineering education through participation in robotics competitions.

In this regard, he has been guiding students of IIT Delhi since 2003 to take part in Doordarshan-Robocon competitions. The team was the champion in 2007 and represented India in the international competition held in Hanoi, Vietnam. To strengthen the concept, Prof. Saha has introduced the concept of Robotics Competition Based Education in Engineering (RoCK-BEE) on which he has already delivered about 58 lectures, and published a fi ction with his student (www.pothi. com). (2) In order to convert engineering problems faced by the rural people of India and the world into research topics or design challenges, and solve them using modern tools like a software or theory, the concept of Multibody Dynamics for Rural Applications or MuDRA was conceived.

This is a short excerpt from the opening of “” by Unknown, quoted for review and introduction purposes. All rights belong to the copyright holders.

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