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No. 35. 'Whippet' safety bicycle. 
This machine embodied the most practical and successful spring-frame ever designed, its great feature being that the relative positions of the saddle, pedals, and handlebar, did not vary, these three points being built up on a rigid triangle, separated from the main frame by a strong coil spring and a movable shackle in the steering mechanism. Thus it was impossible for road shocks, from either wheel, to reach the rider.
On a machine of this type, with cushion tyres, M. A. Holbein beat the 24 hours' road record in 1890, covering 336.5 miles, and beating T. A. Edge who used pneumatics. William Chater-Lea won the Catford open Hill Climb in 1888, 1889, 1891, on 'Whippet' bicycles, at Westerham, Titsey, and Waller Hills respectively.
In the two earlier climbs he rode a spring-frame machine, but in the 1891 event he used a rigid framed 'Whippet.' Chater-Lee acquired his cycle-engineering knowledge as a pupil of C. M. Linley, being employed at the Whippet Works. A letter from C. M. Linley is attached to the exhibit: while claiming that his 'Whippet' spring-frame was a practical and commercial success (a claim which he is entirely justified in making) Linley proceeds:—
“In 1888 the pneumatic tyre appeared, and I recognized that the death knell of the 'Whippet spring-frame had been sounded. The air tyre, by intercepting road shocks before they reached even the rim of the wheel, was a more efficient anti-vibrator device than any contrivance relying on springs in the frame of the cycle itself."
Note the extension on front and rear forks, drilled to carry the mudguard stays, a detail which has been acclaimed as “a modern improvement" 35 years after Linley first used it.
Note also that the toggle joints in steering mechanism have ball-bearings.