2 kinematics of a rigid body

Any point that is rigidly connected to the body can be used as reference point origin of coordinate system L to describe the linear motion of the body the linear position, velocity and acceleration vectors depend on the choice. However, depending on the application, a convenient choice may be: When the center of mass is used as reference point: The linear momentum is independent of the rotational motion. We can hinder the motion of these independent rigid bodies with kinematic constraints. Kinematic constraints are constraints between rigid bodies that result in the decrease of the degrees of freedom of rigid body system.

The term kinematic pairs actually refers to kinematic constraints between rigid bodies. The kinematic pairs are divided into lower pairs and higher pairsdepending on how the two bodies are in contact. A rigid body in a plane has only three independent motions -- two translational and one rotary -- so introducing either a revolute pair or a prismatic pair between two rigid bodies removes two degrees of freedom.

Rigid Body Kinematics

Figure A planar revolute pair R-pair Figure A planar prismatic pair P-pair There are six kinds of lower pairs under the category of spatial mechanisms. Figure A spherical pair S-pair A spherical pair keeps two spherical centers together.

Two rigid bodies connected by this constraint will be able to rotate relatively around x, y and z axes, but there will be no relative translation along any of these axes. Therefore, a spherical pair removes three degrees of freedom in spatial mechanism.

Figure A planar pair E-pair A plane pair keeps the surfaces of two rigid bodies together. To visualize this, imagine a book lying on a table where is can move in any direction except off the table. Two rigid bodies connected by this kind of pair will have two independent translational motions in the plane, and a rotary motion around the axis that is perpendicular to the plane.

Therefore, a plane pair removes three degrees of freedom in spatial mechanism. In our example, the book would not be able to raise off the table or to rotate into the table.

Figure A cylindrical pair C-pair A cylindrical pair keeps two axes of two rigid bodies aligned. Two rigid bodies that are part of this kind of system will have an independent translational motion along the axis and a relative rotary motion around the axis.

Therefore, a cylindrical pair removes four degrees of freedom from spatial mechanism. Figure A revolute pair R-pair A revolute pair keeps the axes of two rigid bodies together. Two rigid bodies constrained by a revolute pair have an independent rotary motion around their common axis.

Therefore, a revolute pair removes five degrees of freedom in spatial mechanism. Figure A prismatic pair P-pair A prismatic pair keeps two axes of two rigid bodies align and allow no relative rotation. Two rigid bodies constrained by this kind of constraint will be able to have an independent translational motion along the axis.

Therefore, a prismatic pair removes five degrees of freedom in spatial mechanism. Figure A screw pair H-pair The screw pair keeps two axes of two rigid bodies aligned and allows a relative screw motion. Two rigid bodies constrained by a screw pair a motion which is a composition of a translational motion along the axis and a corresponding rotary motion around the axis.

Therefore, a screw pair removes five degrees of freedom in spatial mechanism. A constrained rigid body system can be a kinematic chaina mechanisma structure, or none of these. The influence of kinematic constraints in the motion of rigid bodies has two intrinsic aspects, which are the geometrical and physical aspects.The kinematics of a rigid body yields the formula for the acceleration of the particle P i in terms of the position R and acceleration A of the reference particle as well as the angular velocity vector ω and angular acceleration vector α of the rigid system of particles as.

Rigid Body Kinematics. This video is part of the Linearity video series. Write matrices describing rotational components of a real-world, rigid body motion.

Find an expression for a complex rigid body, rotational, time-dependent motion in terms of combinations of simple . Work-Energy (WE) for Rigid Bodies From last class: The WE equation for a system of particles also applies to a system of rigid bodies. TU11 + -2 = T2 center and the rotation of the body.

Kinematics can be a challenge because you need to relate v. Ch. 4: Plane Kinematics of Rigid Bodies Rotation Rotation Rotation of a rigid body is described by its angular motion, which is dictated by the change in the angular position (specified by angle θmeasured from any fixed line) of any line attached to the body.

21 21 21 Example For a short period of time, the motor turns gear A with a constant angular acceleration of ± ² = rad/s 2, starting from rest. Determine the velocity of .

5 Dynamics of Rigid Bodies A rigid body is an idealization of a body that does not deform or change shape. Formally it is defined as a collection of particles with the property that the distance between particles remains unchanged during the course of motions of the body.

EN4 Notes: Kinematics of Rigid Bodies