Most of the methods for planning collision-free robot manipulator arm morions to accomplish collision-free end-effector paths are based on explicit representation of the sub-space of the robot work space that is free of arm motion with obstacles collision. This sub-space is called the robot arm free space and most path planners represent this free space in joint space. If the robot arm free space is represented in joint space, then each point in the free space corresponds to a robot arm configuration for which no arm-obstacle collision occurs. This paper presents a new approach for generating the robot arm free space for an articulated type robot manipulator. This approach uses an oscillating slider crank mechanism for defining the free-space boundary when certain arm-obstacle collisions occurs. The robot arm free space, importantly, is generated in Cartesian space instead of joint space.