No abstract

No abstract

No abstract

Mirror symmetry is an important constraint in 3D reconstruction of an object from a 2D sketch and the subsequent beautification of the 3D model. This paper proposes a new method to detect symmetry planes from a sketch by exploiting the topological connections of the edges it contains. Experiments show that the method can detect all the symmetry planes and the corresponding symmetric vertex pairs, edge pairs and face pairs as well.

An analytical formulation for computing kinematic sensitivity of the spatial four-bar mechanism is presented. The experimental code developed is used to compute an assembled configuration for the mechanism due to a design variation. The mechanism is modeled using graph theory where a body is defined as a node and a kinematic joint is defined as an edge. The spherical joint is cut to convert the model into a tree structure by cutting an edge and introducing constraints. The effect of variation in mechanism design using concepts of virtual displacement and rotation is introduced. The variation of the spherical constraint is computed while maintaining joint-attachment vectors and orientation matrices as variables. A system of equations that has more design variables than equations is then solved using the modified Moore-Penrose pseudo inverse. A recursive formulation is introduced to obtain the state variation of a body in terms of the state variation of a junction body and of the relative coordinates along the chain. The Jacobian matrix is then transformed from Cartesian coordinate space to joint coordinate space using velocity transformation matrices. Kinematic sensitivity analyses due to changing a jointattachment vector and an orientation are presented.