Document Type : Article

**Authors**

Department of Mechanical Engineering, Universidad del Norte, Km.5 Via Puerto Colombia, Barranquilla, Colombia

**Abstract**

Parallel mechanisms with reduced degree of freedom (DOF) have grown in importance

for industry and researchers as they oer a simpler architecture and lower manufactur-

ing/operating costs with great performance. In this paper, a two degree of freedom

parallel robot is proposed and analyzed. The robot with a xed base, a moving platform

and three legs achieve translational and rotational motion through actuation on prismatic

and revolute joints, and can be applied on pick and place applications, vehicle simulators

among others. By making use of homogeneous transformation matrices and Sylvesters

dialytic elimination method a closed form solution for direct kinematics is obtained for

all possible assembly modes. Inverse kinematics was solved in closed form as well. This

greatly decreases computational time and proposed approach is optimal. A case study

was done to validate the solutions found and compared with a CAD model to corroborate

results. Finally, a workspace calculation was made for dierent geometrical parameters

of the robot.

for industry and researchers as they oer a simpler architecture and lower manufactur-

ing/operating costs with great performance. In this paper, a two degree of freedom

parallel robot is proposed and analyzed. The robot with a xed base, a moving platform

and three legs achieve translational and rotational motion through actuation on prismatic

and revolute joints, and can be applied on pick and place applications, vehicle simulators

among others. By making use of homogeneous transformation matrices and Sylvesters

dialytic elimination method a closed form solution for direct kinematics is obtained for

all possible assembly modes. Inverse kinematics was solved in closed form as well. This

greatly decreases computational time and proposed approach is optimal. A case study

was done to validate the solutions found and compared with a CAD model to corroborate

results. Finally, a workspace calculation was made for dierent geometrical parameters

of the robot.

**Keywords**

**Main Subjects**

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Transactions on Mechanical Engineering (B)

July and August 2018Pages 2144-2154