Kinematics Terms Reviewer PDF

Module 1: Introduction Machine: A device that uses forces to accomplish a specific objective. Mechanism: The mechanical portion of a machine that transfers motion and forces from a power source to an output. Link: A rigid body that moves relative to another part in a machine. 4 Joint: A movable...

Module 1: Introduction Machine: A device that uses forces to accomplish a specific objective. Mechanism: The mechanical portion of a machine that transfers motion and forces from a power source to an output. Link: A rigid body that moves relative to another part in a machine. 4 Joint: A movable connection between links that allows relative motion. 5 Structure: An assembly of resistant bodies (members) that carries loads without relative motion between them. Kinematic Pair: Two links or elements in contact with each other, where their relative motion is completely constrained. 7 Constrained Motion: The motion of a Kinematic Pair is limited to a specific direction, either completely, incompletely, or successfully. Inversion of Mechanism: The process of obtaining different mechanisms by fixing different links in a kinematic chain. Kinematic Diagram: A simplified representation of a mechanism used for analyzing motion. Module 2: Kinematics Diagram 1. Degrees of Freedom (DOF):  Definition: The number of independent parameters required to uniquely define the position of a system in space.  Example: A rigid body in plane motion has 3 DOF (2 translations + 1 rotation). 2. Types of Motion:  Translation: Motion where all points of a body move parallel to each other. o Rectilinear: Straight-line path. o Curvilinear: Curved path.  Rotation: Motion around a fixed axis.  Complex Motion: Combination of translation and rotation. 3. Cycle, Period, and Phase:  Cycle: One complete motion sequence of a mechanism.  Period: Time taken to complete one cycle.  Phase: Specific relative positions of a mechanism at a particular time. 4. Links, Joints, and Kinematic Chain:   Link: Rigid body transmitting motion or force. Classified as binary, ternary, or quaternary.  Joint: Connection between links allowing motion. Types include: o Lower Pair: Surface contact (e.g., pin in a hole). o Higher Pair: Point or line contact (e.g., rolling wheels).  Kinematic Chain: A series of links connected to allow relative motion. 5. Mobility:  Definition: The total DOF of a mechanism, calculated using formulas like Gruebler’s equation. Module 3: Vectors 1. Scalar and Vector Quantities:  Scalar: Defined by magnitude only (e.g., temperature, length).  Vector: Defined by both magnitude and direction (e.g., velocity, force). 2. Graphical Vector Analysis:  Definition: A method to visualize and calculate vector quantities using scaled drawings and CAD tools.  Technique: Tip-to-tail method for vector addition. 3. Trigonometric Principles for Vector Analysis:  Right Triangle Relationships: o Basic trigonometric functions: sin⁡,cos⁡,tan⁡\sin, \cos, \tansin,cos,tan. o Pythagorean theorem: a2+b2=c2a^2 + b^2 = c^2a2+b2=c2.  Oblique Triangles: o Law of Sines: asin⁡A=bsin⁡B=csin⁡C\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}sinAa​ =sinBb​ =sinCc​. o Law of Cosines: c2=a2+b2−2abcos⁡Cc^2 = a^2 + b^2 - 2ab\cos Cc2=a2+b2−2abcosC. 4. Vector Manipulation:  Addition: Combining multiple vectors to find a resultant. o Methods include graphical addition and analytical solutions.  Subtraction: Reversing the direction of one vector before addition. 5. Applications:  Used in analyzing forces, motion, and displacement in mechanical systems, often involving problem-solving for angles and distances. Module 4: Displacement 1. Position:  Definition: The spatial location of a point, defined by a position vector RRR from a reference origin to the point’s location. 2. Angular Position:  Definition: The angle a line on a link makes with a reference axis, measured counterclockwise (positive) or clockwise (negative). 3. Displacement:  Definition: The vector difference between the initial and final positions of a point or link. Can be: o Linear Displacement: Straight-line distance between starting and ending points. o Angular Displacement: Change in angular position, measured in degrees or radians. 4. Displacement Analysis:  Definition: Determining the positions of all links in a mechanism as the driver link changes position. Helps in understanding configurations during motion. 5. Quick Return Property:  Definition: A mechanism's characteristic where the return stroke is quicker than the forward stroke. Quantified by the Quick Return Ratio (QRR): QRR=Time of Forward MotionTime of Return MotionQRR = \frac{\text{Time of Forward Motion}}{\text{Time of Return Motion}}QRR=Time of Return MotionTime of Forward Motion​ 6. Maximum Length of Stroke (SmaxS_{max}Smax​ ):  Definition: The distance between the extreme positions of a slider or other moving component in a mechanism. Module 5: Velocity 1. Velocity:  Definition: The rate of change of displacement with respect to time, expressed as: V=ΔRΔtV = \frac{\Delta R}{\Delta t}V=ΔtΔR​ Includes magnitude (speed) and direction. 2. Linear Velocity:  Definition: The velocity of a point moving in a straight or curved path, measured in length per unit time. 3. Angular Velocity (ω\omegaω):  Definition: The rate of change of angular displacement with respect to time, expressed as: ω=ΔθΔt\omega = \frac{\Delta \theta}{\Delta t}ω=ΔtΔθ​ 4. Tangential Velocity:  Definition: The linear velocity of a point on a rotating link, perpendicular to the line connecting the point to the axis of rotation. Calculated as: v=rωv = r\omegav=rω where rrr is the radius. 5. Relative Velocity:  Definition: The velocity of one point relative to another, expressed as: VB/A=VB−VAV_{B/A} = V_B - V_AVB/A​ =VB​ −VA​ 6. Instantaneous Velocity:  Definition: The velocity of a point at a specific instant, often determined graphically or analytically. 7. Proportionality Method:  Definition: A graphical method for determining the instantaneous velocity of points on a mechanism, based on the proportional relationship between radius and velocity. Module 6: Acceleration Acceleration analysis involves determining the manner in which certain points on the links of a mechanism are either “speeding up” or “slowing down.” Acceleration is a critical property because of the inertial forces associated with it. In the study of forces, Sir Isaac Newton discovered that an inertial force is proportional to the acceleration imposed on a body. Linear Acceleration: The rate of change of linear velocity per unit time. It is a vector with direction aligned to motion when accelerating and opposite during deceleration. Angular Acceleration: The rate of change of angular velocity per unit time, expressed in radians per squared second. Positive or negative depending on increasing or decreasing rotational speed. Normal Acceleration: The component of acceleration directed towards the center of rotation, resulting from a change in the direction of velocity Tangential Acceleration: The component of acceleration tangent to the circular path, associated with changes in the magnitude of velocity. Relative Acceleration: The difference in acceleration between two points in motion, accounting for both normal and tangential components. Coriolis Acceleration: An additional acceleration observed when a point moves linearly on a rotating link, defined by the Coriolis effect. ·