Denavit-Hartenberg Parameters
Denavit-Hartenberg Convention for Robot Kinematics · Also known as: DH parameters, DH convention, Robot kinematics convention
The Denavit-Hartenberg (DH) convention is a systematic mathematical method for assigning coordinate frames to the links of an articulated robot or mechanism, enabling compact representation and computation of forward and inverse kinematics. Introduced by Denavit and Hartenberg in 1955, this method uses only four parameters per joint to describe the spatial relationship between adjacent links, dramatically simplifying kinematic analysis and control of complex multi-jointed systems.
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When to use it
Use Denavit-Hartenberg parameters for any robotic or articulated system with multiple joints: industrial robots, robotic arms, gantry systems, or legged machines. It is essential for kinematics simulation, control system design, and programming. Assume the mechanism is rigid with well-defined joints; use this convention when designing or analyzing any articulated linkage.
Strengths & limitations
- Compact, systematic representation requiring only four parameters per joint
- Enables efficient computation of forward kinematics using matrix multiplication
- Provides a standardized notation facilitating communication between researchers and engineers
- Simplifies inverse kinematics derivation for many common robot architectures
- Scales naturally to mechanisms with many degrees of freedom
- Requires careful, consistent frame assignment; errors in parameter definition lead to incorrect kinematics
- Does not directly encode dynamic properties (mass, inertia) needed for control
- Parallel or non-standard joint configurations can be difficult to represent with DH convention
- Numerical singularities and gimbal lock can occur in certain configurations
Frequently asked
What is the difference between the standard DH convention and the modified DH convention?
The standard DH convention assigns the z-axis along the current joint axis, while the modified version assigns it along the next joint axis. Modified DH is sometimes preferred for clarity in representing certain mechanisms, but both are equivalent; choose one and be consistent.
How do I assign DH parameters for a planar 2-link arm?
For a 2-link planar arm with revolute joints: frame 0 at the base, frame 1 at joint 2, frame 2 at the end-effector. Parameters are: a1 (length of link 1), a2 (length of link 2), with zero offset and twist angles. Joint angles theta1 and theta2 are the variables.
What happens if two consecutive joint axes are parallel?
Parallel axes have zero twist angle (alpha = 0). The link offset d then determines the perpendicular distance between the axes. This is a common configuration and the DH convention handles it naturally.
Can I use DH parameters for a robot with closed-loop kinematic chains?
DH parameters are designed for open-chain mechanisms (trees). Closed loops require additional constraints and are typically analyzed using constraint equations or by treating them as redundant open chains with constraints.
Sources
- Denavit, J., & Hartenberg, R. S. (1955). A kinematic notation for lower-pair mechanisms based on matrices. Journal of Applied Mechanics, 22(2), 215-221. link ↗
- Craig, J. J. (2005). Introduction to Robotics: Mechanics and Control (3rd ed.). Pearson Education. ISBN: 0-13-123629-6
- Spong, M. W., Hutchinson, S., & Vidyasagar, M. (2006). Robot Modeling and Control. John Wiley & Sons. ISBN: 0-471-64990-2
How to cite this page
ScholarGate. (2026, June 3). Denavit-Hartenberg Convention for Robot Kinematics. ScholarGate. https://scholargate.app/en/manufacturing/denavit-hartenberg-parameters
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
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