Hiscox illustrates a cam acting at the knee of a toggle linkage. For two equal symmetric links, a transverse knee force is balanced by two link-force components; the ideal axial end reaction is F_k/(2 tan theta).
Toggle-joint Cam Movement Interactive Calculator
Enter an ideal transverse knee force, link angle, link length and an assumed result-scaling percentage. Outputs are illustrative free-body and geometry values, not cam, ram or press capacity predictions.
Equation Used
- Two equal links are symmetric and each makes angle theta with the straight axis.
- Links are ideal rigid two-force members joined by frictionless pins.
- The entered force acts transversely at the knee and the ideal end reaction acts axially.
- The entered length is the pin-to-pin length of one ideal link; h is its perpendicular knee offset L sin theta.
- The percentage is only an assumed multiplier; cam profile, follower direction, motion, friction, clearance, deformation, stress, buckling, drive torque, capacity and safety are omitted.
Cam, Knee and Two Symmetric Links
Gardner D. Hiscox includes a Toggle-joint Cam Movement among cam and press mechanisms. The source drawing establishes the combination of a rotating cam/follower with a knee linkage.
The diagram shows a cam acting on the toggle knee. Its cam motion is schematic; it is not a dimensioned machine or a calculated cam profile.
What This Calculator Does
The tool resolves an entered transverse knee force into the ideal axial reaction at either end of two symmetric links. It calculates the perpendicular knee offset for one entered link length, then applies an entered scaling percentage directly to the ideal force quotient and reaction.
The scaled value is not a real efficiency or machine-output prediction.
Ideal Symmetric-link Equilibrium
R = FkM
Ms = sM
Rs = sR
h = L sin theta
The factor two comes from the two equal link-force components balancing the transverse knee force. Theta is measured from the straight axis and must exceed zero.
Worked Ideal Example
For theta=5 degrees, Fk=500 N, L=100 mm and s=100%, the ideal and scaled quotient is about 5.7, the scaled axial end reaction is about 2.86 kN, and the ideal knee offset is about 8.7 mm.
Those values do not determine a real cam force, ram force, press capacity or safe load.
Assumptions and Limits
- Reference context: rotating cam/follower acting on a toggle-joint knee.
- Calculated: ideal symmetric-link equilibrium, the entered scaling factor and link geometry.
- Not calculated: cam profile, follower contact direction, displacement or velocity, drive torque, energy, dwell, real loss, pin clearance, deformation, stress, buckling, frame or ram strength, tool/workpiece behavior, rated capacity or safety.
Frequently Asked Questions
Why is there a factor of two?
Two symmetric link-force components balance the transverse knee force.
Is the scaling percentage a calculated efficiency?
No. It is an explicit user assumption.
Is the scaled reaction real ram force?
No.
Does knee offset equal ram stroke?
No. It is only L sin theta for one ideal link.
Does the animation solve the cam profile?
No.
Can this size a cam, follower, pins, links, frame, drive or press?
No. Those require full kinematics, loads, materials and applicable safety requirements.
References
- Gardner D. Hiscox, Mechanical Movements, Powers, Devices and Appliances: Toggle-joint Cam Movement.
- University of Maryland, Engineering Mechanics: Statics lecture notes: free-body equilibrium and toggle-mechanism reaction/mechanical advantage.
- U.S. Patent 4,013,003, Press with a toggle joint: two-link toggle topology between a frame and moving ram.
Building or designing a mechanism like this?
Explore the precision-engineered motion control hardware used by mechanical engineers, makers, and product designers.
