A human-robot hybrid cell is developed for performing assembly in flexible manufacturing in collaboration between a robot and its human co-worker. Robot trust in human is considered, a computational model for the trust is derived, and a method to measure and display the trust in real-time is developed. The collaborative assembly includes robot-to-human handovers of payloads (assembly tools). A novel trust-based compliant handover motion planning strategy for the robot is derived. The robot varies its handover configuration and motion based on robot trust in human through kinematic redundancy with the aim of reducing potential impulse forces on human body through payload during handover. A comprehensive scheme is developed to evaluate the collaborative assembly including the trust-based handover strategy. The evaluation results show that consideration of robot trust in human during the assembly and adjustment in handover configuration and motion based on robot's trust levels in human significantly improve human-robot interaction and assembly performance through increasing safety, human trust in robot, handover success rate, and the overall assembly efficiency by 20%, 37.58%, 30% and 6.73% respectively and reducing cognitive workload by 25.63%, with a minor reduction in the handover efficiency by 1.87%.