Line-envelope generations using the concept of instant center

Using the envelope theory to calculate the envelope formed by a family of curves usually requires a tedious mathematical process. This paper presents an alternative approach, which is based on the concept of instant center associated with the vector expressions, for determining the envelope formed by a family of straight lines. Besides effectiveness, this approach yields an intuitive and simplified derivation and also provides better geometric insight into the construction of the resulting envelope. Three examples are provided to demonstrate the nature of this approach.