This paper presents joint space trajectory planning strategy for the legs of 4-DOF parallelogram bipedal robot. The use of two sets of pulley-based parallelogram mechanisms in each leg allows to reduce the number of joint actuators by one in each leg and to keep legs' feet parallel to the horizontal walking surface. By reducing some actuators in the legs design the overall weight, energy consumption and complexity of the robot controller can be reduced. The walk patterns presented in the paper allows the body mass carried by the robot hip (main mass in the robot structure) to be always vertically aligned with the center of the foot area during the single-leg supporting phase of the robot. The transfer of the hip mass from one leg base to another leg base is only permitted during two-legged supporting phase when both legs are firmly in touch with the ground. The idea is to keep the robot as much as possible in static balance condition during the dynamic walk and do not let the hip mass and related gravity force to have a moment arm with respect to the stationary foot center point. The two-dimensional spatial trajectory planning to reduce the ground impact during the legs motion has been derived in joint space coordinates form that would significantly simplify the motor control strategy while implementing the walk patterns and designed trajectories on the physical model. Although the paper does not discuss any issues related to the dynamic walk and dynamic properties of robot, the proper selection of the robot components along with statically optimal positioning of the main body mass (hip mass) of the robot while it walks definitely help to reduce unduly inserted disturbance gravity forces that tends to destabilize the robot.