Title page for ETD etd-09082010-153139

Type of Document Dissertation
Author Ren, Ping
URN etd-09082010-153139
Title Kinematics Analysis of Two Parallel Locomotion Mechanisms
Degree PhD
Department Mechanical Engineering
Advisory Committee
Advisor Name Title
Hong, Dennis W. Committee Chair
Ahmadian, Mehdi Committee Member
Sandu, Corina Committee Member
Sturges, Robert H. Committee Member
West, Robert L. Jr. Committee Member
  • Screw Theory
  • Mechanisms with Variable Topologies
  • Parallel Mechanisms
  • Mobile Robotics
  • Kinematics
Date of Defense 2010-08-27
Availability unrestricted
This dissertation presents the kinematics study on two cases of parallel locomotion

mechanisms. A parallel locomotion mechanism can be defined as “a mechanism with

parallel configuration and discrete contact with respect to the ground which renders a

platform the ability to move”. The first case is a tripedal robot and the second case is an

actuated spoke wheel robot. The kinematics study on these two mobile robots mainly

includes mobility, inverse and forward kinematics, instantaneous kinematics,

singularity and so on.

The tripedal robot STriDER (Self-excited Tripedal Dynamic Experimental Robot)

is expected to walk utilizing its built-in passive dynamics, but in its triple stance phase,

the kinematic configuration of the robot behaves like an in-parallel manipulator. The

locomotion of this novel walking robot and its unique tripedal gait are discussed,

followed by the definitions of its coordinate frames. Geometric methods are adopted for

the forward and inverse displacement analysis in its triple stance phase. Simulations are

presented to validate both the inverse and the forward displacement solutions. The

instantaneous kinematics and singularity analysis are developed respectively. Based on

the screw theory, the Jacobian matrices are assembled. Using Grassmann Line

Geometry, each row of the Jacobian matrices is interpreted as a line in 3D space and the

analytical conditions of the linear dependency cases are identified, which corresponds

to the forward singular configurations of the robot.

The actuated spoke wheel robot IMPASS (Intelligent Mobility Platform with Active

Spoke System) is investigated as the second case. It is revealed that this robot has

multiple modes of locomotion on the ground and it is able to change its topology by

changing the contact scheme of its spokes with the ground. This robot is treated as a

mechanism with variable topologies and Modified Grübler-Kutzbach criterion and

Grassmann Line Geometry are adopted to identify the degrees of freedom (DOF) for

each case of its topological structures. The characteristic DOF are then verified through

the testing on the robot prototype. The forward and inverse kinematics is investigated

for two cases of its topologies. In order to improve the computation efficiency of the

inverse kinematics formulation, virtual serial manipulator models are constructed. The

effectiveness of the virtual serial manipulator models has been validated with numerical


In conclusion, kinematics analyses have been successfully performed on the two

parallel locomotion mechanisms. The results are utilized to control the robots’ motions

in specific configurations. The foundation has been laid for the future development of

the robot prototypes and the future research on dynamics, control, intelligence and so


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