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Bishop, Robert H. - The Mechatronics Handbook [CRC Press 2002] Part 7

Tham khảo tài liệu 'bishop, robert h. - the mechatronics handbook [crc press 2002] part 7', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Fundamental Concepts Angular Displacement Velocity and Acceleration The concept of rotational motion is readily formalized all points within a rotating rigid body move in parallel or coincident planes while remaining at fixed distances from a line called the axis. In a perfectly rigid body all points also remain at fixed distances from each other. Rotation is perceived as a change in the angular position of a reference point on the body i.e. as its angular displacement A0 over some time interval At. The motion of that point and therefore of the whole body is characterized by its clockwise CW or counterclockwise CCW direction and by its angular velocity ũ Aỡ At. If during a time interval At the velocity changes by Aũ the body is undergoing an angular acceleration a Aũ At. With angles measured in radians and time in seconds units of ũ become radians per second rad s- and of a radians per second per second rad s- . Angular velocity is often referred to as rotational speed and measured in numbers of complete revolutions per minute rpm or per second rps . Force Torque and Equilibrium Rotational motion as with motion in general is controlled by forces in accordance with Newton s laws. Because a force directly affects only that component of motion in its line of action forces or components of forces acting in any plane that includes the axis produce no tendency for rotation about that axis. Rotation can be initiated altered in velocity or terminated only by a tangential force Ft acting at a finite radial distance l from the axis. The effectiveness of such forces increases with both Ft and l hence their product called a moment is the activating quantity for rotational motion. A moment about the rotational axis constitutes a torque. Figure 19.45 a shows a force F acting at an angle p to the tangent at a point P distant l the moment arm from the axis. The torque T is found from the tangential component of F as T Ftl F cos b l 19.58 The combined effect known as the resultant