An eight-bar linkage contains eight rigid bodies, including its fixed frame. The Jansen-type leg shown here uses a rotating crank, four connecting rods, two rigid triangular members and the frame. One crank turn drives the foot around a closed path.
The calculator solves the pin positions from constant link lengths. It shows the actual foot path, its horizontal and vertical ranges, path distance and speed. Both triangular members retain their shape throughout the cycle.
Eight-bar Linkage Interactive Calculator
Adjust a Jansen-type leg’s scale, crank radius and speed. Every pin follows its fixed-length constraints, and the foot path is calculated from the same geometry.
Equation Used
- Eight rigid planar bodies including the chassis.
- Seven pin locations represent ten equivalent revolute joints.
- Constant crank speed; one full turn per gait cycle.
- All lengths scale together, with crank radius separately adjustable before scaling.
- Selected continuous assembly branch throughout 12–16 mm crank range.
- No ground-contact, friction, structural or motor-load model.
A physical eight-body leg: two rigid triangles, four rods, one crank and the fixed chassis.
Follow the eight rigid bodies
The fixed chassis joins P1 and P2. The crank rotates around P2, taking P3 with it. Rods P3–P4 and P3–P6 drive the upper triangular rocker P1–P4–P5 and the lower rocker P1–P6. Rod P5–P7 connects the upper triangle to the lower triangular member P6–P7–P8. P8 is the foot.
Each triangle is one rigid link, even though its outline has three sides. That gives one fixed body, one crank, four rods and two triangles: eight bodies altogether. The model follows the topology in Nansai, Elara and Iwase’s figure 2. The numerical dimensions here are rounded teaching values, not an exact set of Strandbeest construction dimensions.
There are seven physical pin locations, P1 through P7. Three locations—P1, P3 and P6—join three bodies each, and each of those counts as two two-body revolute joints. The remaining four count once. The mobility calculation therefore uses ten equivalent revolute joints.
Explore the walking-leg path
Whole mechanism scale changes all lengths together. It changes the size of the foot path while preserving its shape. Crank radius changes the shape as well as the range of the path. Crank speed sets cycle time and foot speed; at zero rpm the mechanism stays still and its complete path remains visible.
The displayed path is measured relative to the fixed chassis. Its near-horizontal lower portion can be useful when designing a walking leg, but the calculator does not force the foot onto a ground line. Actual body travel, slipping, clearance, load support and coordination between several legs require a separate ground-contact model.
Eight-bar mechanisms form a broader family, with different topologies and coupler paths. This page uses one specific leg so every drawn link and input has a clear physical meaning.
Mobility, circle intersections and foot speed
The planar mobility count is M=3(n−1)−2j, where n includes ground and j counts equivalent one-degree-of-freedom revolute joints. Here n=8 and j=10, giving M=1. This count assumes independent constraints and does not itself guarantee a particular set of lengths can complete a rotation.
Pin locations are found from intersecting two circles. For centers A and B separated by d, and link lengths r and s, distance along AB is x=(r²−s²+d²)/(2d), and the perpendicular offset is h=√(r²−x²). A fixed choice of intersection side maintains the selected assembly throughout the cycle.
At scale 1, the fixed points are P1=(0,0) and P2=(38,8) mm. Crank P2–P3 is adjustable from 12 to 16 mm. The remaining dimensions in mm are P1–P4=42, P3–P4=50, P1–P5=40, P4–P5=56, P1–P6=40, P3–P6=62, P5–P7=40, P6–P7=37, P6–P8=49 and P7–P8=66. All are multiplied by the selected whole-mechanism scale.
The horizontal range is max(x₈)−min(x₈); vertical range is max(y₈)−min(y₈). Path distance is the sum of distances between successive foot positions sampled at quarter-degree crank intervals. At speed N rpm, cycle time is 60/N seconds and mean foot-path speed is path distance×N/60.
Current speed is the norm of the differentiated foot position multiplied by crank angular speed. Constant crank speed generally produces varying foot speed. The path dimensions and extrema are numerical estimates from the sampled linkage positions.
Example: scale 1, 15 mm crank and 12 rpm
The selected leg has a horizontal foot range of approximately 68.65 mm and a vertical range of 16.69 mm. One crank revolution traces approximately 145.15 mm of foot travel relative to the chassis.
At 12 rpm, a cycle takes 5 seconds and mean foot-path speed is about 29.03 mm/s. Current speed changes around the path. Doubling mechanism scale doubles the path dimensions and speeds at the same rpm; doubling rpm halves cycle time without changing the geometric path.
Reducing the crank radius to 12 mm changes the path to approximately 55.03 mm wide and 7.48 mm high. That comparison illustrates why changing one bar length can alter gait shape, rather than simply making the same motion smaller.
Model assumptions and limits
All link lengths and both rigid triangular shapes remain constant throughout the selected continuous assembly. The allowed crank range has been checked through a full rotation. Bars cross in the side view because they occupy different parallel layers; a crossing without a white pin is not a joint.
The calculation covers planar kinematics. It does not estimate motor torque, pin loads, bearing friction, structural deflection or tolerances. The fixed-chassis animation is not a complete walking-robot simulation, and the vertical foot range is not automatically the available clearance over an obstacle.
Rigid triangular plates make the body count explicit and avoid counting their edges as independent moving links. Different constructions may use three braced bars for the same triangle; mechanically, a rigid triangle still acts as one body for this analysis.
Eight-bar linkage questions
Why are there only seven visible pin locations?
Three pins each join three bodies. Each represents two equivalent two-body joints, so the total constraint count is ten.
Is each side of a triangular member a separate link?
No. The three corners stay fixed relative to one another. The complete rigid triangle counts as one body.
Does a one-degree-of-freedom count guarantee a complete turn?
No. Mobility counts constraints. Lengths and assembly branch must also permit the requested positions. The selected dimensions and crank range here have been checked through the full cycle.
Does the green path show the machine moving forward?
No. It shows foot motion relative to the fixed chassis. Ground contact and body motion are not imposed.
Are these exact Jansen fabrication dimensions?
No. They are stated, rounded teaching dimensions for the same linkage topology. Use the model to understand the kinematics, not as a completed structural design.
Primary references
Shunsuke Nansai, Mohan Rajesh Elara and Masami Iwase, Speed Control of Jansen Linkage Mechanism for Exquisite Tasks, 2016, figure 2 and section 2: linkage topology and circle-intersection position analysis.
Aaron L. Guo, University of Texas Robot Mechanism Design, II. Design Process, 2022: a built Jansen leg using rigid triangular members and layered joints. Dimensions and calculator implementation on this page are independently specified.
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