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Arm robot manipulator heavily applied in industries ranging from welding, pick-and-place, assembly, packaging, labeling, etc. Trajectory planning and tracking is the fundamental design of an arm robot manipulator. The trajectory is set and determined to satisfy a certain criterion effectively and optimally. Optimization of robot trajectory is necessary to ensure the good quality product and to save energy, and this optimization can be provided by the right modeling and design. This paper presents a review study of arm-robot manipulator design and control for trajectory tracking by investigating the modeling of an arm robot manipulator starting from kinematics, dynamics and the application of the more advanced methods. The idea of this paper comes from the popularity of inverse kinematics among students.