Motion given by circular trajectory and circular envelope

Planar kinematic geometry

© doc. Ing. Ivana Linkeová, Ph.D.

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Specification of a motion

The following rules are valid for a motion given by circular trajectory τ^A of point A and circular envelope (b) of straight line b:

- Point A is located on trajectory τ^A at each instant.

- Straight line b is a tangent line of envelope (b) at each instant.

- Point A is the intersection of straight line b and trajectory τ^A.

This motion and the motion given by circular and linear trajectories are inverse motion.

Animation of a motion (motion given by circular trajectory and circular envelopa)

Fixed centrode (motion given by circular trajectory and circular envelope)

Trajectory of a point (motion given by circular trajectory and circular envelopa)

Envelope of a circle (motion given by circular trajectory and circular envelopa)

Envelope of a straight line (motion given by circular trajectory and circular envelopa)

Specification of inverse motion (motion given by circular trajectory and circular envelopa)

- Point A⁰ becomes the point envelope of trajectory τ^A; the centre of circle τ^A moves along circle with centre at point A⁰ and radius equal to the radius of trajectory τ^A.

- Straight line b⁰ becomes the envelope of envelope (b); the centre of circle (b) moves along straight line parallel to straight line b⁰ passing through the given centre of envelope (b).

- The distance between the centre of moving trajecotry τ^A and the centre of moving envelope (b) does not change during the motion.

Moving centrode (motion given by circular trajectory and circular envelopa)