A novel approach to the kinematic coordination problem for dual-arm robots and for the definition of bimanual tasks is proposed, where both modelling and control aspects of the problem are handled using dual quaternion representation of pose and screw-based manipulator Jacobian. The proposed formulation is advantageous in terms of computation and storage efficiency compared to other formulations of dual-arm manipulator forward kinematics and Jacobian computation. Unit dual quaternion representation is also capable of avoiding representational singularities related to orientation. The coordination problem for dual-arm manipulation is addressed using relative Jacobian, and parametrized task definition is achieved using virtual mechanisms and task-specific Jacobians. The framework hence developed has been validated using a dual-arm Baxter robot for steering wheel rotation and bimanual pouring tasks, thus validating the position controller with both relative and global task-space motions. The proposed experiments use a visual sensing strategy to detect and follow the manipulated objects during the task.