Introduction Sometimes, a body has simultaneously a motion of rotation and translation, such as a wheel of a car, a sphere rolling (not slipping) on the ground. In actual practice, the motion of link AB is so gradual to see both. Instantaneous Centre of Rotation A combined motion of rotation and translation of link AB may be assume to be in pure rotation about some centre I, known as instantaneous centre of rotation (also called centro or virtual centre)

Instantaneous Centre of Rotation As points A and B moves to A1 and B’ therefore position of centre of rotation must lie on the intersection of the right bisectors of chords A1A and B1B. Let the bisectors intersect at I. We see position of the link AB goes on changing, therefore the centre about which the motion is assumed also goes on changing. Instantaneous centre of a moving body may be defined as that centre which goes on changing from one instant to other. The locus of all such instantaneous centres is known as centrode. A line drawn through instantaneous centre and perpendicular to the plane of motion is instantaneous axis.

Types of Instantaneous Centres Instantaneous centres are of three types: Fixed Instantaneous centres. Permanent Instantaneous centre Neither fixed nor permanent Instantaneous centres. The first two fixed and permanent instantaneous centres are together known as primary instantaneous centres. The third type is known as secondary instantaneous centres. Consider a four bar mechanism ABCD as shown in diagram. The number of instantaneous centres are given by formula

Types of Instantaneous Centres The instantaneous centres I12 and I14 are called as the fixed instantaneous centres. They remain in the same place for all configurations of the mechanism. The instantaneous centres I23 and I34 are of permanent nature. They moves when the mechanism moves. The instantaneous centres I13 and I24 are neither fixed nor permanent , as they vary with the configuration of mechanism. Note: The instantaneous centres of two links such as link 1 and link 2 is usually denoted by I12.

Location of Instantaneous Centre Following rules may be used to locate the instantaneous centres of the mechanism. When two links are connected by pin joint (or pivot point), the instantaneous centre lies on centre of pin as shown in (a). Such instantaneous centre is of permanent type but if one link is fixed the instantaneous centre will be of fixed type. When two links have pure rolling contact (link 2 rolls without slipping upon fixed link 1 which may be straight or curved), the instantaneous centres lies on point of contact as shown in (b). Velocity of any point A on link 2 relative to fixed link 1 will be perpendicular to I12A and is proportional to I12A.

Location of Instantaneous Centre When two links have sliding contact the instantaneous centre lies on the common normal at the point of contact. When link 2 moves on surface link 1 the instantaneous centre lies at infinity and each point on slider have same velocity. When link 2 slider moves on curved surface link 1, the instantaneous centre lies on centre of curvature of the curvilinear path. When slider link 2 moves on fixed link 1 having constant radius of curvature, the instantaneous centre lies at centre of curvature that is the centre of circle.

Aronhold Kennedy’s Theorem When three bodies move relative to one another they have three instantaneous centres all of which lie at the same straight line. Consider three kinematic links A,B and C having plane relative motion.

Method of Locating Instantaneous Centre First of all, determine the number of instantaneous centres by formula Make a list of instantaneous centres in mechanism. Since four bar has six instantaneous centres as shown below.

Method of Locating Instantaneous Centre Locate the fixed and permanent instantaneous centres by inspection. In figure (a) I12 and I14 are fixed instantaneous centres and I23 and I34 are permanent instantaneous centres. Locate the remaining centres by Kennedy’s theorem. Draw circle diagram. Mark points on a circle equal to number of links in a mechanism. Mark 1,2,3 and 4. Join the points by solid lines to show that these centres are already found. In circle diagram these are 12,23,34 and 14 to indicate centres I12,I23,I34 and I14.

Method of Locating Instantaneous Centre To find other two centres join two such points that they form two adjacent triangles in circle diagram. Join 1 and 3 to form triangles 123 and 431. instantaneous centre I13 will lie on intersection of I12I23 and I14I34. Similarly draw a line between 2 and 4. mark it as 6 to show I24 .

End of Lecture 4 Thank You!